There are a host of options:
1) To replace your amp, try a Tech 21 Sansamp Character series pedal. loads of different flavours of amps available, very tweakable, also with defeatable speaker emulation now.
2) To replace your whole pedal board, the HD series from Line6 is hard to beat for an all in one budget solution
3) To perhaps just go for your amp sound but more controlled, an isobox or a well-placed shield can help.
4) Powerscaling - if your guitarists wants true control over his sound AND needs reasonable breakup, check out London Power Scaling - can be added to almost any amp and allows you to get full power tube saturation at most any level. It's not a load or anything like that. It scales the power output of the power amp. Also, once you reduce it down to less than about 1-3W, you don't need a load - I just use a Palmer Speaker Sim DI box (PDI-09). I contacted London themselves to confirm this works before trying it, and he ran me through the mathematics of it. So with a small head/combo and this you don't need a speaker... but the DI also has a speaker out, so you could have that as well.