You would really have to check with them to see what they will let you do. There are too many moving parts for anyone to guess.

I know for a fact that you can move securities from one rollover IRA to another. But even if the general answer for a 401k is yes, you're still going to have to check with your particular 401k provider. (Do they allow you to transfer securities? Are the particular funds that you have even something that can be transferred and not something proprietary? Does your employer block you from transferring securities until you leave the company?)