There are two approaches to upgrade Pega instance with multiple applications.
1. "Out of Place upgrade" - If client is ready to upgrade all applications at once, we can use this approach. Set up a cloned environment of the Dev and run the upgrade scripts (migrate.sh and upgrade.sh) to perform the upgrade. To do upgrade of the sub sequent higher environments we can use "Lift and Shift" approach i.e. copy upgraded rules schema from lower env. and then run the data only upgrade to upgrade the existing schema. More details can be found from Platform Upgrade guide.
2. "Install and Migrate approach" - Say there are 5 applications present in the instance and client only wants to upgrade 2 applications out of 5. To do this, Create a fresh Pega7 installation and import the RAP of the selected applications. In future when remaining applications needs to be upgraded, we can import the RAP of the remaining applications. To do upgrade of the sub sequent higher environments we can use "Lift and Shift" approach as stated above.
When using 'Lift and Shift', we have to ensure that code bases of all the environments are in sync (as we are coping upgraded rule schema from lower to higher envs.).
More information related to running the scripts and do the upgrade can be found from the platform upgrade guide, PFB url