It depends on the exact fan capabilities / motor type / bulb or light type.
There are “universal” kits which even license Bond technology - basically the same Smart by Bond tech I mentioned earlier that some fans come with built in to their proprietary receivers.
You can read here some of the pros and cons of the Bridge (what you have right now) vs Smart by Bond aftermarket kits; for your particular model, you could swap out to the universal kit sold at Home Depot or other retailers and retain 4 speeds on fan but I am not certain you’d get light control over the LEDs - I think those universal kits usually just control how much current goes to the light kit for older style filament dimmable bulbs.
It may be something you want to look more into for future purchases to see if the fan has Smart by Bond built in or if it is marketed as compatible, and/or sold, with Bond Bridge.
Some brands are mentioned here, but I don’t think it is every model that uses the Smart by Bond embedded tech.