The tires size can be changed while keeping the same rims. How much, is something you would want to ask a tire rep (butler tire, discount tire, etc). To answer your second question, no you don't have to run a staggered step (example below). I recently switched to a non staggered setup without any problem.

I suggest that you go directly to a tire dealer and ask what size will fit on your current wheels. The rest is all preference.

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2005 545i Sports/Prem Package
(Retired) 2003 X5 4.4i-sport package, cold weather package, OEM trailer hitch, 20' replica metallic pewter 215's, X-pipe, Navi w/ custom splash (MUFC logo), cross drilled brembo rotors with Akebono ceremic pads.