I have a 2018 JK Wrangler (see signature). We set it up ourselves for flat towing about a year ago using a Blue Ox base plate like you are talking about doing (ours has the stock bumper so it worked fine). I definitely understand what you're asking, and can relate to the dilemma. :)
Without knowing the specifics of the aftermarket bumper your Jeep has, it is very difficult to say with certainty if the Blue Ox plate would be compatible with it or not.
I've seen a couple aftermarket Jeep bumpers that are compatible with blue ox base plate, many (most) that are not, and a few that require some cutting or other modifications to the bumper in order to fit a blue ox base plate under it. Just which of those categories yours would fall under, is tough to say without seeing your front end, bumper up close.
If you can find out who makes the aftermarket bumper you have, you might try reaching out to them and see if they can tell you whether a blue ox base plate will fit under it or not. If thats not possible, I would just look real closely at your current bumper, how far down it goes, and compare that with instructions/illustrations from the blue ox base plate. You might be able to determine for yourself if this is doable or not.
There are some aftermarket bumpers for Jeeps, that you can attach tow hooks directly to it that will connect directly to your tow bar. I didn't go that route, but sometimes really wish I did. Every now and then I think about ditching the blue ox base plate and putting on a cool front bumper that you can attach tow bar directly to. You may want to consider going that route.