Wife has company stock, want to move from current brokerage to ? Not sure next step

My wife currently has shares in her company stock. Credit Suisse is the brokerage but we want to move it out, maybe diversify into other stocks. Is this something we can do on our own? Manage our own stocks? I was looking at Robinhood but they don't have the brokerage transfer in that we'd be looking for.

Any advice would be great!

Thanks!