diff --git a/.euts.env.example b/.euts.env.example
index 34281aa..58575a5 100644
--- a/.euts.env.example
+++ b/.euts.env.example
@@ -13,9 +13,10 @@
 
 ### Containers Runtime Settings
 
-# The project name is used as prefix for the name of the containers that will be built.
-# This allows to build and run different copies of the stack in parallel
-#TESTSTACK_PROJECT_NAME=euts
+# The project name is used as prefix for the name of the containers and images that will be built.
+# This allows to build and run different copies of the stack in parallel.
+# It is also used as part of the name of the custom composer 'vendor' dir that will be used.
+#COMPOSE_PROJECT_NAME=euts
 
 # Custom Timezone for the containers. Use 'none' as null value
 #TESTSTACK_TZ=none
diff --git a/WHATSNEW.md b/WHATSNEW.md
index c7f9325..9266c7d 100644
--- a/WHATSNEW.md
+++ b/WHATSNEW.md
@@ -1,3 +1,10 @@
+Version 0.3 (unreleased)
+========================
+
+* fix: make it possible to run multiple copies of the stack in parallel.
+  In order to achieve this, env var TESTSTACK_PROJECT_NAME has been replaced with COMPOSE_PROJECT_NAME in config file .euts.env.
+  In order to retain Backwards Compatibility, the old variable name is still accepted if the new one is not used.
+
 Version 0.2
 ===========
 
diff --git a/bin/setup/composer-dependencies.sh b/bin/setup/composer-dependencies.sh
index d971c68..634c557 100755
--- a/bin/setup/composer-dependencies.sh
+++ b/bin/setup/composer-dependencies.sh
@@ -3,7 +3,7 @@
 # Install dependencies using Composer
 # We do not rely on the requirements set in composer.json, but install a different eZ version depending on the test matrix (env vars)
 #
-# Uses env vars: EZ_COMPOSER_LOCK, EZ_PACKAGES, TESTSTACK_PROJECT_NAME, TRAVIS
+# Uses env vars: EZ_COMPOSER_LOCK, EZ_PACKAGES, COMPOSE_PROJECT_NAME, TRAVIS
 
 # @todo generate and echo a hash which can be used to determine in the future if we need to run composer again (as it
 #       would install different packages compared to the ones installed currently)
@@ -29,8 +29,8 @@ if [ -n "${EZ_COMPOSER_LOCK}" ]; then
 else
     echo "Installing packages via Composer: the ones in composer.json plus ${EZ_PACKAGES}..."
 
-    if [ -n "${TESTSTACK_PROJECT_NAME}" ]; then
-        export COMPOSER="composer_${TESTSTACK_PROJECT_NAME}.json"
+    if [ -n "${COMPOSE_PROJECT_NAME}" ]; then
+        export COMPOSER="composer_${COMPOSE_PROJECT_NAME}.json"
         cp composer.json ${COMPOSER}
     fi
     # we split require from update to (hopefully) save some ram
diff --git a/doc/config_examples/bundle_with_extra_dependencies/.euts.113.env b/doc/config_examples/bundle_with_extra_dependencies/.euts.113.env
index cbc6f13..75194a8 100644
--- a/doc/config_examples/bundle_with_extra_dependencies/.euts.113.env
+++ b/doc/config_examples/bundle_with_extra_dependencies/.euts.113.env
@@ -1,7 +1,7 @@
 # Example TesStack configuration for testing Kaliop eZMigration Bundle on eZ Platform 1
 
 # Use a specific project name - always a good idea when you plan to test the same bundle in different configurations
-TESTSTACK_PROJECT_NAME=kezmbt_113
+COMPOSE_PROJECT_NAME=kezmbt_113
 # Debian Stretch comes with php 7.0 by default. We need php 7.1 minimum for ezplatform-matrix-fieldtype
 TESTSTACK_DEBIAN_VERSION=stretch
 TESTSTACK_PHP_VERSION=7.1
diff --git a/doc/config_examples/bundle_with_extra_dependencies/.euts.23.env b/doc/config_examples/bundle_with_extra_dependencies/.euts.23.env
index 127f378..02eff42 100644
--- a/doc/config_examples/bundle_with_extra_dependencies/.euts.23.env
+++ b/doc/config_examples/bundle_with_extra_dependencies/.euts.23.env
@@ -1,7 +1,7 @@
 # Example TesStack configuration for testing Kaliop eZMigration Bundle on eZ Platform 2.3
 
 # Use a specific project name - always a good idea when you plan to test the same bundle in different configurations
-TESTSTACK_PROJECT_NAME=kezmbt_23
+COMPOSE_PROJECT_NAME=kezmbt_23
 # We use Debian Buster which comes with php 7.3 by default
 TESTSTACK_DEBIAN_VERSION=buster
 
diff --git a/doc/config_examples/bundle_with_extra_dependencies/.euts.25.env b/doc/config_examples/bundle_with_extra_dependencies/.euts.25.env
index 6075151..ce9d6fd 100644
--- a/doc/config_examples/bundle_with_extra_dependencies/.euts.25.env
+++ b/doc/config_examples/bundle_with_extra_dependencies/.euts.25.env
@@ -1,7 +1,7 @@
 # Example TesStack configuration for testing Kaliop eZMigration Bundle on eZ Platform 2.3
 
 # Use a specific project name - always a good idea when you plan to test the same bundle in different configurations
-TESTSTACK_PROJECT_NAME=kezmbt_25
+COMPOSE_PROJECT_NAME=kezmbt_25
 # We use Debian Buster (which comes with php 7.3 by default) and php 7.4
 TESTSTACK_DEBIAN_VERSION=buster
 TESTSTACK_PHP_VERSION=7.4
diff --git a/doc/config_examples/bundle_with_extra_dependencies/.euts.cp.env b/doc/config_examples/bundle_with_extra_dependencies/.euts.cp.env
index f3d535f..e4b754f 100644
--- a/doc/config_examples/bundle_with_extra_dependencies/.euts.cp.env
+++ b/doc/config_examples/bundle_with_extra_dependencies/.euts.cp.env
@@ -1,7 +1,7 @@
 # Example TesStack configuration for testing Kaliop eZMigration Bundle on eZ Community Project (5.4)
 
 # Use a specific project name - always a good idea when you plan to test the same bundle in different configurations
-TESTSTACK_PROJECT_NAME=kezmbt_cp
+COMPOSE_PROJECT_NAME=kezmbt_cp
 # Use Debian Jessie for the container OS as it comes with php 5.6 by default
 TESTSTACK_DEBIAN_VERSION=jessie
 
diff --git a/docker/docker-compose-mysql.yml b/docker/docker-compose-mysql.yml
index ab8151a..2545e2f 100644
--- a/docker/docker-compose-mysql.yml
+++ b/docker/docker-compose-mysql.yml
@@ -3,7 +3,7 @@ version: '3'
 services:
 
     mysql:
-        image: ${TESTSTACK_PROJECT_NAME:-euts}_mysql
+        image: ${COMPOSE_PROJECT_NAME:-euts}_mysql
         build:
             context: images/mysql
             args:
@@ -11,10 +11,10 @@ services:
                 # note: Travis Xenial and Bionic images come with mysql 5.7 by default; Focal comes with mysql 8.0
                 #       But mysql 5.6 is not recommended for EZP 5.4, so we default to 5.6
                 mysql_version: ${MYSQL_VERSION:-5.6}
-                project_name: ${TESTSTACK_PROJECT_NAME:-euts}
+                project_name: ${COMPOSE_PROJECT_NAME:-euts}
                 timezone: ${TESTSTACK_TZ:-none}
         hostname: mysql
-        container_name: ${TESTSTACK_PROJECT_NAME:-euts}_mysql
+        container_name: ${COMPOSE_PROJECT_NAME:-euts}_mysql
         environment:
             - CONTAINER_USER_UID=${CONTAINER_USER_UID:-1000}
             - CONTAINER_USER_GID=${CONTAINER_USER_GID:-1000}
diff --git a/docker/docker-compose-postgresql.yml b/docker/docker-compose-postgresql.yml
index 2a7ed93..ef24808 100644
--- a/docker/docker-compose-postgresql.yml
+++ b/docker/docker-compose-postgresql.yml
@@ -3,7 +3,7 @@ version: '3'
 services:
 
     postgresql:
-        image: ${TESTSTACK_PROJECT_NAME:-euts}_postgresql
+        image: ${COMPOSE_PROJECT_NAME:-euts}_postgresql
         build:
             context: images/postgresql
             args:
@@ -11,10 +11,10 @@ services:
                 # note: Travis Xenial images come with PG 9.4-9.6,10; Bionic with 9.3-9.6,10,11 and Focal with 12
                 #       We go with 9.5 as default because it is the lowest upstream supported version as of 11/2020...
                 postgresql_version: ${POSTGRESQL_VERSION:-9.5}
-                project_name: ${TESTSTACK_PROJECT_NAME:-euts}
+                project_name: ${COMPOSE_PROJECT_NAME:-euts}
                 timezone: ${TESTSTACK_TZ:-none}
         hostname: postgresql
-        container_name: ${TESTSTACK_PROJECT_NAME:-euts}_postgresql
+        container_name: ${COMPOSE_PROJECT_NAME:-euts}_postgresql
         environment:
             - CONTAINER_USER_UID=${CONTAINER_USER_UID:-1000}
             - CONTAINER_USER_GID=${CONTAINER_USER_GID:-1000}
diff --git a/docker/docker-compose.yml b/docker/docker-compose.yml
index 7cf267e..5af039d 100644
--- a/docker/docker-compose.yml
+++ b/docker/docker-compose.yml
@@ -3,7 +3,7 @@ version: '3'
 services:
 
     ez:
-        image: ${TESTSTACK_PROJECT_NAME:-euts}_ez
+        image: ${COMPOSE_PROJECT_NAME:-euts}_ez
         build:
             context: images/ez
             args:
@@ -11,10 +11,10 @@ services:
                 debian_version: ${TESTSTACK_DEBIAN_VERSION:-buster}
                 do_update_os: ${TESTSTACK_UPDATE_OS_ON_BUILD:-true}
                 php_version: ${TESTSTACK_PHP_VERSION:-default}
-                project_name: ${TESTSTACK_PROJECT_NAME:-euts}
+                project_name: ${COMPOSE_PROJECT_NAME:-euts}
                 timezone: ${TESTSTACK_TZ:-none}
         hostname: ez
-        container_name: ${TESTSTACK_PROJECT_NAME:-euts}_ez
+        container_name: ${COMPOSE_PROJECT_NAME:-euts}_ez
         environment:
             ## Configuration used by the boot/setup scripts
             - COMPOSER_AUTH
@@ -22,7 +22,7 @@ services:
             - CONTAINER_USER_GID=${CONTAINER_USER_GID:-1000}
             - http_proxy
             - https_proxy
-            - TESTSTACK_PROJECT_NAME
+            - COMPOSE_PROJECT_NAME
             - TESTSTACK_SETUP_APP_ON_BOOT
             ## Database configuration
             - DB_TYPE=${DB_TYPE:-mysql}
diff --git a/docker/images/ez/root/boot/symlinkvendors.sh b/docker/images/ez/root/boot/symlinkvendors.sh
index 544e470..0de970e 100644
--- a/docker/images/ez/root/boot/symlinkvendors.sh
+++ b/docker/images/ez/root/boot/symlinkvendors.sh
@@ -11,7 +11,7 @@ CONTAINER_USER_HOME=$(echo "$ORIGPASSWD" | cut -f6 -d:)
 #    # @todo to avoid generating uselessly different variations, we should as well sort EZ_PACKAGES
 #    TESTSTACK_VENDOR_DIR=vendor_$(echo "${P_V} ${EZ_PACKAGES}" | md5sum | awk  '{print $1}')
 #fi
-TESTSTACK_VENDOR_DIR="vendor_${TESTSTACK_PROJECT_NAME}"
+TESTSTACK_VENDOR_DIR="vendor_${COMPOSE_PROJECT_NAME}"
 
 # @todo we assume that /home/test/bundle/vendor is never a file...
 
diff --git a/teststack b/teststack
index c8fc722..0fde2d3 100755
--- a/teststack
+++ b/teststack
@@ -258,6 +258,11 @@ dotenv() {
     set -a
         . "${1}"
     set +a
+
+    # BC with versions 0.1 - 0.2
+    if [ -z "${COMPOSE_PROJECT_NAME}" -a -n "${TESTSTACK_PROJECT_NAME}" ]; then
+        export COMPOSE_PROJECT_NAME="${TESTSTACK_PROJECT_NAME}"
+    fi
 }
 
 load_config() {
@@ -442,7 +447,7 @@ cd $(dirname -- ${BASH_SOURCE[0]})/docker
 
 # Since the line below relies on knowing the contents of the yml file anyway, let's be more efficient...
 #WEB_CONTAINER=$(${DOCKER_TESTSTACK_QUIET} config | grep 'container_name: .*_ez$' | sed -e 's/ \+container_name: \+//g')
-WEB_CONTAINER=${TESTSTACK_PROJECT_NAME:-euts}_ez
+WEB_CONTAINER=${COMPOSE_PROJECT_NAME:-euts}_ez
 
 case "${COMMAND}" in
     build)