You can transfer positions "all in kind" from brokerage to brokerage. Depending on the relationship they have it will take 10-20 business days with a period of approx. 1-3 business days where you won't be able to trade. Additionally, every time you do trade pre-transfer completion/ post transfer initiation, it will delay the process.
Just did it...I had to liquidate my Fidelity Penny Stocks...Etrade will not except a Transfer of Penny Stocks coming in from another Brokerage...Not sure about you scenario but I'm thinking you must liquidate 1st