Can you put a different size tire on the same rim? Yes, you can if you understand some measurements. Tires are measured in three aspects. Section width, sidewall height (as a percentage of width), and the inner bead diameter (such as 15, 16, 18 inches).
A 225/60R/16 tire has a width of 225mm, a sidewall which is 60% of 225mm, and it's bead is just 16 inches. You can substitute tires that have the same diameter but with some limits. This is often done for performance reasons or to change how your car looks.
The first is the ratio between the rim width and tire width. As another answer points out, you can put a tire with a wider section (tread) width only up to a certain point-which sometimes isn’t clear or obvious since tread width is measured in millimeters (mm), while rims (in America anyway) are often measured in inches.
If your rim width is 7 inches, that’s 177mm, but tires come in 165, 175, and so on in 5mm increments. Most 7 inch rims can safely drive on 215, or even 225mm when properly inflated. A 7.5-inch rim can usually handle up to 245 or 255mm.
But going up a section width also usually means going down in aspect ratio. Our hypothetical 225/60R/16 tire can be replaced with a 235/55/16 or 245/50/16 and still have the same overall outside diameter. You can find other information on https://zero60times.com/
When you buy a tire, it's important to measure the inside of the wheel well for clearance. If the tire is too wide or tall and rubs against something that might not be safe like brake lines or suspension connections, then there might be a problem. The tire could get damaged and not work as well. It could also not leave enough space to evacuate water or snow from the wheel wells.
The other important consideration is the pressure rating.
If you drive on tires with a lower pressure rating than what was originally installed, then it could cause problems like tire overheating or even blowouts because of faster than normal speeds for that type of tire.
That said if the rims are all labeled as requiring 215/45R17, then theoretically because they are all smaller than 225/50R17 (the max diameter), only tires in that range should be used to maintain proper overall circumference and ensure there's enough pressure.
There might also be clearance issues with alloy wheels due to their thicker centers compared to steel wheels which usually have some space between them and the rubber so water can escape. The alloy center might have a different diameter than the steel rim.
This is to prevent uneven wear and possible vibrations from driving on tires with diameters that are too different from what was originally installed as original equipment by the manufacturer or recommended as an alternate replacement size by a tire professional because of any other factors such as sidewall height, speed rating, etc.
In summary, if you want to put a larger-section width tire on your car it may fit but you will increase its circumference and therefore decrease its ability to match up with how many revolutions per mile that type of tire needs to travel at the intended speed for which it was designed. On some cars this can trigger serious problems like increased noise and vibration at freeway speeds.