Having trouble with sound deadening

My theater is in the basement and I have A LOT of soundproofing. It works well for mids and highs, but the bass still shakes the room upstairs. The structure of the home is transferring the bass. Is there any way to deaden the structure of the house?
Not easily but there are devices, passive or active, that will absorb bass energy.
What is your goal? Acoustical isolation or sound quality?
What have you done so far?
Mass, distance, and de-coupling (the least of these three) are the variables that are in play for lessening bass transfer. Unfortunately, bass hitting hard surfaces will vibrate all through the rest of the structure. Bass waves are also VERY LONG, and will easily go through drywall/joist structures, and pass to the next adjoining spaces.
It's not easy to isolate the bass, without dealing with the entire space. Building a studs/drywall "room within a room" structure in the existing basement, will actually help the sound out in a lot of aspects, but cause other compromises potentially. Still, if you can't decouple the room from the upstairs, you'll have little success in your endeavor.
Lots of info on doing just this on forums, sound treatment webpages, pro audio acoustics papers, home theater architect write-ups, etc.
How far are you willing to go here? ..is what I'd ask myself
Yes, if the room is finished with sheetrock you remove the sheeetrock and extend it away from the studs with absorbing material instead of screwing the sheetrock directly to the studs.

The more absorbing material you have the higher you have to turn up the volume and the higher you turn up the volume the more absorbing material you will need.
I'd suggest reading Premium Home Theater by Earl Geddes. It's well written and easy to understand, and it nicely lays out the theory of room acoustics and specific solutions. You've already hit on the major problem of the structure transferring vibrations to other rooms. I think the most effective solution would be to incorporate resilient channels into your walls and ceiling that physically decouple the sheet rock from the studs, beams, etc. (floors could be a tougher problem if not on a cement slab). Not a small job but not horrible either. If you're handy you could probably tackle it yourself with a helper. Or, alternatively, the book is detailed enough that any competent contractor should be able to do it (i.e. you don't necessarily need someone who specializes in audio rooms and is really expensive). Either way, I suggest reading the book because it will help you understand the underlying issues and probably with the rest of your room's acoustics as well. I found it extremely interesting and educational, and it was by far the best of the several books I bought on the subject (at least for a layman like me). Best of luck.
I recommend a couple of bass shakers. Too much bass from powerful sub could hurt listenersÂ’ ears. Young people's ears are easy to damage! The bass shaker is more effective and fun to feel the action in the movie. They are quiet, small, cheap and easy to install. Bass shakers should be attached under the sofa or listening chair. Then you just need no or one small powered sub with low volume at night.
Look up Quiet Rock_ to add t your existing drywall. Do not remove existing drywall- waste of money. add to what you have. Resilient bars, with quiet rock---incredible improvement!!! 2 or three treatments will stop train rumbling by!!!
Bass moves in mysterious ways in a room. There are almost always peaks and nulls that occur in a particular space. One thing to try is to move your sub or subs to a different part of the room. That can change the way bass energy is transferred to the rest of the house. Also try them near field closer to the couch. That way you can turn down the sub volume and still get the bass response you are looking for.

Acoustic measurements would help to understand the problem.

Everything else is guessing.

Audyssey XT32 has a low frequency filter that can be applied to minimize those bass notes that easily disturb people in neighboring rooms.

If you get a AVR or Pre/Pro with the XT32 in it (not the regular Audyssey, it has to be the XT32), it may help the situation.
Been in the insulation business for over 40 years and I completely agree with Avgoround. Good Luck

Auralex subwoofer platform as suggested, or spring isolation are possible solutions to decouple mechanically the sub.

Personally I use springs. (common knowledge to many in Agon now)