Others have pointed out that if your current set up runs continuously and you can’t get to the goal temperature, then turning the thermostat down won’t matter. It doesn’t run “faster or harder”, it just runs at the same pace longer until it hits the goal - or in your case, never.
As has been suggested: seal leaks and cracks, more insulation above (and below, if appropriate), double pane windows.
Speaking of windows, if you have a lot of them, consider tinting or shading to alleviate the heat coming in. Having a company apply tinted film can be costly, but you can do it yourself if you’re moderately handy, and after you screw up one or two you’ll get the hang of it.
Quick fix: stand-alone inside air conditioner, to be used only in the room where it’s located (must have port to exhaust hot air through a window.) Very effective, but can be loud.
Adding a mini-split would be less expensive, even DIY for $1K, $3-$6K for professional installation, and can add significant capacity at relatively low cost. You need somewhere to put that big hanging white blob on the wall, tho.
Because we have a wall of South facing windows, we added motorized awnings which make a huge difference in keep the sun’s heat out when it’s at its worst. They go out on calm days only, unfortunately, but mostly when it’s cloudy it’s not so bad anyway.
Lots of things you can do, fighting over the thermostat is probably the least productive.
{Edit: You might also schedule a visit from your HVAC company to make sure your system is working at max efficiency. I’m sure they’re swamped, pardon the pun, but at the very least, go out side and see if the outside air handler is blocked by plants or pollen or something else which reduces efficiency. You can hose it off to clean it.}
