You don't have to be rich to cross train, just need to be able to commit the time and the mental discipline to stick to things. Most places in my experience will offer a range of flexible payment options and packages to suit most everyone. When I tried Krav Maga, the cost was $15 a fortnight on a 1 year contract but that included a full kit of gear (helmet, mouth/shin/forearm/elbow/chest guards, grappling mitts, hand wraps, boxing gloves and the most important thing IMO - a solid groin guard)
I've since stopped KM and have recently looked at a boxing gym - classes haven't officially started yet because of ongoing issues with insurance to do with actual sparring and matches but the cost is $10 a fortnight and I just need my own bag gloves, hand mitts/wraps and mouthguard; all of which I have anyway. That fee also allows me full use to the entire gym plus any other classes they run such as Yoga, Pilates, Les Mills type stuff, Tai Chi and BJJ.
Something like the second if accessible to yourself shouldn't strain the finances too badly and still offer you a chance to face off against other opponents. Keep in mind though, as has been said before: you will not be using Tai Chi Quan against boxing or BJJ, you will be learning a whole new system and adding to your skillset. If you can bring in aspects from your primary art and make them work within the framework of the secondary art, that would be a huge plus
EDITING TO ADD: Final point I'd like to put forth is that while enthusiasm is a great thing, I might suggest choosing several arts to crosstrain with at the outset will actually be detrimental to your learning. You've got a base in Tai Chi Quan, pick one other thing (Boxing/BJJ/Whatever) and stick to just those 2 for another year or 2 at a minimum. Once you get the basics down pat in both, if you still feel the need to, re-explore your options concerning more/other arts you might like to look into and experience. I doubt anyone here will give you flak if after a year you decide boxing isn't your thing and move onto something else.