After spending way too much time trying to find my notes on past research, I've attempted to consolidate the key info in one place. This will be a little sloppy of the cut and paste from my files and pictures since my tables don't want to come across clean. Feel free to add your setup details & note any errors I might have made. Some of this might be controversial but this is my Opinion from my experience along with info from this Forum and my research. Most of this should hold for all of the AMG Models including the 53 Coupe, 53 SUV and the 63S SUV. This is a little late for anyone researching a winter set but there's always next year
Here are some specs of OEM GLE AMG 450; GLE AMG 53; GLE AMG 63S Wheel sizes and offset:

20”-RZV/RZW 20” AMG 5 SPOKE 275/50 R20 Front 9J ET57 & Rear 9J ET44 (Front is wider than the rear by almost ½”)
21”-RWD/RWE 21” AMG Twin 5-Spoke Wheel....Front-275/45 R 21 on 10 J x 21 ET51 & Rear-315/40 R 21 on 11 J x 21 ET47
22”-RXU/RXV 22” AMG Cross-Spoke Wheel....Front-285/40 R 22 on 10 J x 22 ET55/56 & Rear- 325/35 R 22 on 11 J x 22 ET53/52
GLE 167.xxx Bolt pattern 5X112 Stud bolt M15-1.25 threads-Ball seat. Most Aftermarket wheels have Conical seat stud bolts.

1. Mercedes runs staggered wheels on 21” & 22” (Front 10”, Rear 11”) but it’s almost impossible to find matching wheels of similar widths and then with the proper offsets. The aftermarket has not caught up with specs for the GLE 53 & 63S yet. As soon as I receive my GLE 53 with Red brakes, I will be able to confirm that my winter set up on 20 inch wheels will fit. This discussion focuses primarily on the front because that’s the primary fitment challenge.
   
2. Tire tread position will remain centered with the wheel irrespective of wheel width.
3. As the wheel width is reduced, the section width (bulge) will increase but the tread and tire diameter remain relatively constant. The industry rule of thumb is that for every 1/2" change in rim width, the tire's section width will correspondingly change by approximately 2/10". More bulge can improve ride but probably not that much on larger wheels with reduced sidewall height & higher air pressures. A rim that is too narrow in relation to the tire width can allow the tire to distort excessively sideways under fast cornering.
4. Wheel Offset-Mercedes wheels come OEM on the GLE with high offset numbers with fronts in the 50’s, rears in the 40’s. The challenge is finding Aftermarket wheels with higher offsets. Intuitively we tend to think that a higher number moves the wheel out from the car but it’s just the opposite. Offset is measured in mm-6.35mm= ¼”.
   
5. There should be no fitment risk from lower offsets that move the wheel out away from the brakes and other suspension parts except for the fender clearance and potential rubbing when turning. I found a “rule of thumb” noting that most cars will accept up to 1/2” wider from stock but it’s best to make your own calculation if a vendor hasn’t already got fitments listed.
   Some will argue that moving too much wider could affect the vehicle’s handling. There is some advantage to having the leverage point to the outside of the wheel. Most of us won’t notice any difference with small changes, IMO.
   
6. Tires are very limited for the larger wheels, 21’s have few options for Mercedes sizes. If you want a narrow winter tire you can use a tire size calculator to compare to OEM specs and get close to the same tire circumference. I had to do this on another vehcile to get the winter tire I wanted...not available in the factory size. Mercedes specs the rear tire sizes on 10” & 11” wheels with sizes that calculate very near the same circumferance.. As you reduce the tire width (1st#) just try calculating using higher a 2nd number that is a % of the tire width to see how the tire compares to the OEM one.
   

All US wheels are DOT approved so personally I don’t get hung up on aftermarket quality if they are from a reputable source. A Flow formed wheel is a better wheel than a cast, flow formed (forged) are generally lighter and stronger. They are also more limited in supply and styles. I think the factory AMG 21’s are cast & the 22 Cross Spoke are forged.
RIM WIDTH RANGE-"A tire's rim width range identifies the narrowest to the widest rim widths upon which the tire is designed to be mounted during its tens-of-thousands of miles and years of service." Here are some for OEM tire ranges.
Sources-

Offset calculator: Use Greg’s tool posted next....

Tire Size Comparison Calculator: https://tiresize.com/calculator/

Lug bolts-Otis LA, Ebay, Google M15x1.25 Lug bolt

 

I think this is the best wheel/tire sizing tool: http://www.rimsntires.com/specspro.jsp

You can put it the stock specs and then compare other offsets/sizes easily.

 

Much better tool-already found some errors in my calculations. Thanks Greg....