I soup my HP5+ in HC-110 if I'm using medium or large format. With rotary development at a pretty high dilution, I get an EI of 250 for sufficient shadow detail. I think HC-110 gives a really nice look to the film. Very classic, a smooth and pleasing grain structure, and lots of highlight tone separation. In 120 and up, the grain won't be particularly visible anyway unless you're printing very large.
I have pushed HP5+ to ISO 3200 in HC-110 dilution A once. It had okay shadows but of course ridiculous grain and contrast.
However, I don't do push processing or make attempts to shoot HP5+ at higher than box speed in any format these days; I just use it for what it is. If I was going to try and get extra film speed out of it, I would probably use XTOL. In 35mm, I sometimes develop my HC-110 in Mytol at stock strength (which is a DIY clone of XTOL and gives essentially identical results). The grain is smaller but slightly less smooth, and I get full box speed of 400. Results are a bit sharper. Again, that's probably irrelevant in formats larger than 35mm.
If you're really serious about getting hyper fast film speeds, you would probably want something along the lines of Diafine, which is specifically for that purpose. I expect you'd be able to get ISO 1600 or thereabouts with usable contrast in Diafine, but that's a shot in the dark, as I have no firsthand experience with the combo. I've just heard that TriX at 1250 in Diafine is considered a tried-and-true recipe, so I'm extrapolating and thinking HP5+ is probably similar.
Rodinal stand development might get you up somewhere in the neighborhood of 1000 too. But stand development comes with its own set of risks (bromide drag, uneven development), especially in 120. And personally I've never much cared for HP5+ in Rodinal. It's grainy in a way that seems harsh and gritty to me, which isn't a look I'm really ever going for. The contrast and tonality just seem really "meh" to me as well.
Anyway, TL;DR:
Diafine if speed is your priority
XTOL for fine grain at box speed
HC-110 for flexibility and a really nice look
Those would be my recommendations.