Theoretically, how large/massive can a rocky planet be?

I’m aware that once it gets massive enough, it would start capturing gases and turn into a gas giant. But let’s imagine a scenario where a bunch of rocks keep clumping together with no end and with no gases around. How large could the planet get? how massive? What would happen if it’d keep amassing more rocks? Would it compress into plasma and turn into a star? At which point would that happen?