I had this same urge a while back as well but took a different approach by using a track bike geo and had a road frame built around that.

As others have mentioned rear spacing of a track bike is 120mm. If you wanted to use modern gears you would need to have the rear spaced at 130mm. If you have a modern aluminium or carbon track bike that would be one major hurdle.

Another thing mentioned was cable stops. Problem solvers makes a bunch of clamp on options but they really do look nasty.

Then there is that thing called brakes. Since geared bikes have a freewheel you loose that ability to slow down the bike with your legs so hand brakes are sorta needed.

Track bikes aren't drilled for brakes (well at least the ones I ride) so you're going to have to either get those clamp on adapters for the front fork or hope you're really good at drilling. They have an option that straps the rear brake underneath the rear stays but like the cable stops, they just make the bike look nasty.

There's more to it than just begin able to bolt on a rear derailleur and at the end of the day you probably ruined a decent track bike and ended up with a meh road bike and probably spent more than just buying a dedicated road bike.