You can use a thicker gauge material, but I disagree with the other answer and would steer away from stainless steel.
If moving from aluminum, which you don't have to, one of the perks of materials such as copper, freedom gray, lead coated copper, even galvanized steel (although I don't recommend the last one) is that you can solder all joints. You can solder stainless, but it is extremely hard in vertical seams, near impossible, so you can forget about soldering. So you essentially have a much better material, but the same riveted / screwed / caulked joints.
Another thing to think about is reflection. You would need to try to get a finish on stainless that would not be extremely reflective like #8, but even a 2B / 2D finish will be, and that may even cause damage with heat, melting or burning things.
If you want an upgrade from regular aluminum gutters, get something custom made, in a thicker gauge, like an 0.050" or a 0.063".
Want something even better, get something you can solder like copper gutters. If you worried about the color, get lead coated copper, which can be easily painted.
Sheet Metal / Roofing Companies are specialized in this, and will help you develop profiles and custom manufacture what you need.
Normal gutter machines will not accept much thicker gauges than usual so you may end up with something custom, brake formed.
Same goes for downspouts, when brake formed, any feasible, custom size can be made.