Pull Chain Fan

Actually, thinking more about it, this assumption may not be valid. If power comes into the switch box, it may be split into two separate loads at that point - traditionally one on a black wire and one on a red wire. One would be controlled by the switch and the other would be connected to the line supplying the switch. If so, you would be able to control both by replacing the single gang box with a two gang and connecting one switch to each wire. It’s more work than replacing a switch but less than running new wiring.

Here’s some more discussion of this option: