If you belong to more than one project, you should see the corresponding unix group IDs typing the linux command groups on your shell.
By default, you are logged with the unix group of your primary project. However, you can temporarily change your current group ID to a different one with the command newgrp.

newgrp man page 
DESCRIPTION
       The newgrp command is used to change the current group ID during a login session. If the optional - flag is given, the
       user's environment will be reinitialized as though the user had logged in, otherwise the current environment, including
       current working directory, remains unchanged.

If wish to write on the project folder of a secondary group of yours (e.g.: group ID sXYZ), first you will need to change group ID using the command newgrp sXYZ.
Then you will be able to write on the corresponding project storage folder sXYZ using the corresponding quota.

For more details on the commands groups and newgrp, please have a look at the linux man pages typing the commands man groups  or man newgrp respectively.

Please read as well the documentation dedicated to file systems available on the CSCS Knowledge Base