Can I put a smaller size tire on staggered rear rims which will allow me to use the same size tire on all four staggered rims?

The problem you have is that your rear wheels are wider than your front wheels, so your rear rims are wider than your front rims. You can't put a narrower width tire on a rim than it is designed for as it won't make contact with the rim.

You could get narrower rims for your car, I wouldn't recommend it because you have a powerful rear wheel drive car and the extra width gives more grip so your rear end is less likely to break free. If you put narrower rims on you increase the likelihood you'll end up wrapped around a tree.

I did a quick search on a couple of tire sites for your tire sizes and found at least 20 choices for summer, winter and all season categories from many different brands and price ranges, so it seems like you probably have some choice. It's not important to have the same tire brand or model on front and rear, you just need tires that match up reasonably well in type and rating so they give similar grip, so don't change your rims just so you can have the brand or model of tire.

As your car is 4 wheel drive, it's important to keep to outside diameter the same to avoid abnornal load and wear on the centre diff/transmission. The width is not as important.

This site shows a 0.6% difference in OD with your current tyres.

As Paulster suggested you could buy a 2nd set of rims specifically for winter tyres. And there shouldnt be any risk going to the same width front & rear. Winter/snow tyres are typically higher profile and narrower than standard.

I'd reccomend to talk to a Mercedes dealer for reccomendations and then look for competitive alternatives. It's important to get the correct size, stud pattern and offset for your car.

One advantage of having winter rims is that it saves your nice factory rims from being eaten by salt & grit. Also being able to swap and store them means you'll get better useful life out of the tyres.

Note: Some countries require tyres to match left/right & front/rear. Check the legal requirements for where you live.