Security clearance continuation

Can you maintain or ‘freeze’ the any part of the clearance process and have it continued by another employer? Given they are similar clearances, different sponsors.

I don’t think you can freeze anything. But the new sponsor should be able to take over the investigation. Did you ask the CSO at the new sponsor?

Yes, a new potential employer can pick up your investigation in the pretty much the same way that they can pick up your clearance once you are cleared.

YOU don’t do this your self. The new employer needs to do it.