Knowledge Base Help & Documentation:

How many migrations can I run simultaneously using CMS2CMS?

So to answer the question: Can I run multi-website migrations at the same time?
Well in short the answer is yes!
The CMS2CMS migration wizard can only manage a single migration at a time.
To run another migration simultaneously under your account you will need to open the wizard in another browser tab.

You cannot run multi migrations for the same source and target sites simultaneously. Your migration will fail if you do so.