Is it possible to double the resistance of a potentiometer?
With the newly added original schematic, we can see that this is a RC oscillator circuit. To achieve your real goal of adding a half tempo switch, we can divide the tempo in half by adding a second capacitor with the same value as the original one. With the switch the resulting circuit segment would look like this: 







simulate this circuit &ndash; Schematic created using CircuitLab

When the switch is closed the capacitance is doubled, which means the frequency is halved. That sounds by far like the easiest option here - much easier than replacing the potentiometer with anything.