Correct setup second console for one PSN account

I have a Pro and would like to add a PS4 Slim to host a 24/7 Minecraft server. The problem is, those world saves are tied to a specific account, so I'd have to use that one on the Slim. But I also want to use that same account on the Pro as it has my trophies etc. Is there anyway to have the same account logged on to two systems simultaneously?