does frequency multiplier work with signal that contain multiple frequency components?
It will contain 330 and 450MHz.

But it is not linear so it will also contain


110+150
330+/-150
450+/-110


and all the other possible combinations of the input frequencies and harmonics. 

This is called intermodulation.

It will then contain the intermodulation products from those frequencies eg. (450-110)+150

etc, etc ad infinitum these are 2nd,3rd nth order intermods. The higher order intermods fall around the wanted signal, unlike the harmonics, so you can't filter them out.

The whole process in non-linear i.e as the 150MHz gets stronger , the intermodulation mess gets dramatically worse