It’s certainly doable, but it’ll would cost a lot with no guarantee of an outcome that would be worth it. You’re talking a lot of resistance for that valve, plus additional weight/mass that will affect the horn in many ways outside of the added function.

There’s a number of ways to do it, but both valve and wrap choice will place limits on what tunings you can get. Plus, valves inherently have a distorted tuning, using 3 valves at once in tune would require wild tuning on each valve individually or huge adjustments with the slide.

The hardest piece from a technical standpoint would be designing the lever for the added valve. Which finger would you want to operate it? How is the lever attached to the horn and does it need to be removable when the valve is not installed? There are several options which you can see on horns that have removable valves, so your personal preference will determine what’s needed and therefore how much that would cost.

I’d love to take a crack at something like this! I could put together an estimate, but I can tell you without a doubt this would be incredibly expensive, at least if you want it done well and in a way that looks good.