Investing Across Stages

You should look up The Chernin Group (TCG)

Insight Partners (depending on how software-y you want to go) and TCV also might be decent to add to your list - Sixth Street has some groups that might be appealing as well. Growth runs a little different there (but mostly because its largely driven by converts).

Bessemer just launched a growth buyout fund on top of the early stage practice they already had

CPP’s Thematic investing team checks all those markers. However, they are a pension (though to me that is a plus!)

An unconventional take, but would think about a lateral move to Raine. Between their various venture / growth funds, they'll do everything from seed to pre-IPO; you'll probably never see them doing a vanilla LBO, but they have a mix of Series C+ venture growth deals and traditional bootstrapped growth equity (more buyout-esque, control positions possible). Main industries of focus are gaming, music, e-commerce, digital content, live events, etc. - so essentially anything consumer / media.

Only caveat is that you'll need to split time between investing and banking (mostly cap raises and M&A advisory), which some might enjoy but others won't. 

Your best options are either some sort of family office (I did something similar) or a sector-focused fund or strategy that invests across stages.

You won’t find buyout, but I think a lot of tech crossover shops would fit what you want - Dragoneer, Greenoaks, etc. Obv. incredibly competitive but fit the flexible mandate (less buyout) that you want (and pay very well)

I guess a bigger question you should be asking yourself though is why you want a flexible mandate? On the one hand, it sounds sexy and it hypothetically gets you a wide range of skills. On the other hand, it also spreads you very thin and leaves you scrambling to really figure out what you enjoy and what you’re good at.