Problem with MOSFET making my current dissapear
If you can find a multiplexer with a high current limit then yes, that is possible. Many chips have a 50mA limit, and multiplexers are typically not used for switching current. It would be better to find a high side switch configuration with a logic level input like this (There should also be integrated high side switches if you need compactness with the current level you desire):


Source: 3.3v high side switch

Instead of 12V in this circuit, you could use the regulated 150mA current source. You would need one of these circuits for each of your loads (which is an LED?).