not really sure what it is that you are making... but adding another moving component to the head can only hurt rigidity.

I think your best bet would be to machine what you can in one setup and maybe make a fixture that can hold your semi finished part and has a pick point so you can finish the part.

Or like others have said, go for a bigger mill ! Not sure if there is another maker of mini \ benchtop sized machine in the US?

Andrew