Yes you can. The MIT and BSD licenses explicitly allow sublicensing. That's part of their whole schtick and why free software people don't particularly like them (you can sublicense them to be proprietary).
The MIT license explicitly (um, er, literally, explicitly) allows sub-licensing by mentioning it. The BSD does not mention sub-licensing, so I wouldn't say it explicitly allows it. But yeah, it effectively allows it, of a fork anyway.
