Lots of sense in the other responses. Here’s where I’d start - get an accurate scale and weigh the combo on the car now. Look for 15x7 and 16x7 wheel/sticky-hi-po-tire combos that weigh the same or less (preferably) than what you have on there now. 205 section in a sticky tire will provide a big positive hit in grip. If you keep the combo lighter you’ll see better acceleration, braking and your spring/damper combo will be more responsive. Whatever you do - don’t throw a 215 or 225 section tire on that 6” wheel thinking things are gonna substantially improve. Overall performance will likely be worse. The BMW test mentioned earlier (and a C&D VW test of 15’s-18’s) illustrated what happens when much heavier wheel/tire combos go on a car.

A couple of years ago, I removed the 195/50/16 OEM wheels/tires from my 2015 Honda Fit - weight 37.5 lbs. each. I replaced them with a Kosei Racing lightweight wheel (9.5 lbs) and a Goodyear 195/70/13 tire - weight - 23 lbs. each. A 14.5 lb. reduction at each corner of the car. I saw a well documented 10% improvement in highway fuel mileage (40-42 up to 44-46) and 13% improvement in around town mileage (30-32 to 34-35). Acceleration notably improved; suspension response felt like I'd bolted on a set of Eibach/Koni coilovers. Focus on the weight of your new combo -- and the stickiness of the replacement tire if you want more cornering/braking grip. Tire Rack has lots of detailed weight info on all their wheels/tires. Do not mount a 215 or 225 tire onto that 6" wheel and expect to see improved performance.
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82 242-6.2L; '17 Mazda3; '16 Crosstrek

Check with a good indie tire shop, they have a book that will tell you the largest tire size for your rims.

Unfortunately, tire makers have virtually abandoned performance tires for wheels that are 15 inch or smaller.

Larger wheels DO NOT mean better performance.

Better tires do.

Formula 1 wheels are quite small by today's standards. They are 13 inch wheels! But wide.

A few years ago Road & Track did a test of +1, +2, and +3 wheels on a BMW 3 series.

They did a skid pan and a lap time test with 15, 16, 17, and 18 inch wheels.

They used the same model of performance tires of each size.

The best performer - the original 15 inch wheels!

They asked a BMW engineer about the surprising results - He said - Of course, we designed the suspension for 15 inch wheels.

R&Ts conclusion - when people get bigger wheels, they also add newer, and often better tires as well - the tires account for the improvement, if any.