Probably at first sight you haven't noticed, but it is only allowed a unique Mass Transfer ID per environment/tier. So, for instance, if you have the Migration Cockpit project with the Mass transfer ID M05 at client 001 in development, in this environment it will be unique.
But what about if I want to use this project in the development Client 002?
This is a tutorial about how to use the same Migration Cockpit project in different clients from the same environment. The step-by-step is done in the Migration Cockpit 2020.
File/Stagging approach
execute the transaction code LTMOM and
select the project you want to use in the client you want to use.


go to: "More" --> "Goto" --> "Use Project in a Different Client".

Execute.

select "continue".

if you have more than one project with the same name (but different Mass Transfer ids), in this Migration Cockpit version (sp 12) you will get an error, but the change will be performed successfully.
Note that if you have several projects with the same name, but different Mass Transfer ID you will get this message:

Don't worry because this is a bug that does not impact in the client change.

Don't forget that from the Fiori side (preparing the data, validate the data mapping, and simulation) the migration process needs to be done all over again in the new client.
Direct Approach
For the direct approach, the process is the same as it was for transporting to a different environment. So you will need to add the project to be changed to a transport package.
I hope this post is valuable for you!