Min 4 signal pins and 2 power pins.
Power 8A continuous 12A peak.
Can use additional signal pins for power if needed.
Greetings,
It may cost a bit extra in terms of overall acreage and airspace, but a person may want to take a look at bottom-entry variants of the otherwise-typical square-pin header, putting the socket half on the “outside” of the sandwich so just the insulation on the pin half has to fit within the stack height. Multi-source options might be within reach going this route.
Failing that, product in the Arrays, Edge Type, Mezzanine (Board to Board) family would be the next likely place to look around.
Some more targeted suggestions may emerge if you’d care to expound a bit on your needs and tradeoff considerations.