Is it still generally expected to fully deploy a fund before starting the next one?

Assume that all conventional wisdom is either old or wrong. Now, there may be contractual rules that prevent a general partner from raising a new fund before deploying an old fund. Outside of contractual limitations, it is very common to see general partners deploy and raise at the same time. It is hard to do. Think about it this way. If you are deploying and raising at the same time, then your are deploying from Fund 1, raising Fund 2 AND possibly also deploying from Fund 2, all simultaneously. That's tricky.