Designing an allpass IIR filter with arbitrary phase response
Depends a bit on what exactly you are trying to do. Generally, strict all-pass filters have reciprocal zeros and poles. This will always result in 180 phase shift per filter order so an arbitrary phase response that's strictly allpass cannot be designed. Example: let's say you want something that's in phase at DC,  sits at -90 degrees in the band and then goes slowly back to zero at Nyquist: this can't be implemented using strict all-passes.

Of course you can always approximate but the best method tends to depend on the specifics of your design problems and what types of errors you can tolerate.