I think part of the problem is here is that those of us who are inexperienced with wheels and tires and more casual auto enthusiasts sometimes confuse the terminology.
I have the factory all-season wheel package all around, with 225/40R18 tires - Pirelli Cinturato P7 all season run-flats.
BMW "my garage" tells me the original factory specs by vin for this car included:
18" Double-spoke wheels, style 436M wit h all-season run-flat tires
And there is a PDF at this link:
https://www.2addicts.com/forums/show....php?t=1132609
That shows that I most likely have code 2TR style 436M (front/rear 18.75 225/40 R18) factory wheels (and I'd need to find a set of factory code 2PG, style 436M rear wheels if I wanted to go 18x8, 245/35 R18 staggered while keeping my factory front wheels.)
The confusion for people like us wo aren't gearheads comes in that the tires are measured in mm (225... 245) and the wheels are measured in inchs (18x7.5 front - 18.8 back).
And that wheels often get called rims - and tires often get called wheels, casually.
I've experienced the back "swaying" in my 16 F23 when merging onto the highway and accelerating hard... it didn't feel like tramlining. I've owned a 97 Mustang GT 4.6 and this feels different - it isn't like the wheels are trying to follow road-ruts - it is like a sway. Even accelerating hard without changing lanes - the back feels like it wants to track in a different direction than the front. I've seen posts of other 235i drivers here describe what sounds like nearly the same experience. I've also heard stories in the past about tuned Bugs, Audi TTs and Porsche Boxsters requiring more rear downforce because of the short wheelbase and aerodynamics tending to make the rear come out at high speeds. The first time I had heard about this was back in the late 80s when I was a teen that owned a tuned Datsun 510 - a friend described tuned Bugs basically having the rear end come all the way around and the whole car spinning circles down the track because they weren't aerodynamically designed to do speeds over 50 MPH. Later when the TT came out, the earliest versions did not have a rear tail, but it was quickly added - and the Porsche Boxster's automatic tail pops out at highway speeds for this reason.
The feeling is also different than the twitchiness of the rear end of an M4 when you stomp on it and it tries to keep all that torque sticking to the ground - different than when you hit a bump or joint expansion in a corner and the back end skips around. The feeling of breaking loose didn't happen at the START of acceleration or during a gear shift with the M235i, but in the middle of it. It also isn't just me - I had my wife test drive it when I bought it and she commented on the same feeling. I don't have it as bad as the other poster - my DSC light isn't coming on just during hard acceleration on the on-ramp, or anywhere else - but the feeling of sway during enthusiastic driving is noticeable.
I figure the first time I take it in for service I'm going to have them look at the rear suspension - and I'll probably take it in for a 4 wheel alignment - but I hate alignment issues - I feel like often alignment is a symptom of something else wrong with the suspension, and just correcting the alignment is an expensive band-aid if you don't fix the problem causing that issue.
And in this case, the advice I've heard makes me wonder if it is just a matter of the tires being square when they should be staggered, and all-season run-flats instead of traditional summer tires.
I'd like a big, open flat surface that I could really open it up on without any walls to put it into if I spun to really get a feel for what is going on.
Anyhow, at the end of this, I realized it kind of was thread hijacking - but I'm in a similar boat to OP with wanting to replace factory wheels - only the reverse - I want to go staggered - and the links I provided may help OP or anyone else reading along who is seeking a similar solution.