LED signals for Atlas turnouts

Does anyone know how to use an Arduino to control indicator LED using Atlas model RR turnout machines. That is, I want to activate momentary button to trigger solenoid to change turnout and change panel LED and signal LED. Change polarity and push button to turn off LED and on another LED. How many turnouts can be operated on one Arduino? Not all at same time. This is a DC curcuit, not a DCC circuit.

An Uno (as an example) has 20 IO pins. So 20 would be the theoretical maximum for the Uno. The MEga has a lot more but it's still limited.

You can use shift registers (e.g. 74HC595 for outputs, 74HC165 for inputs) or port expanders to 'create' more IO.