For many designs the stackup and material type is critical, and at Royal Circuits we can help you in the design process. Changing the stackup is easy to modify down to .003 layer to layer spacing. The design should dictate the stackup and not the other way around.
Here are the standard stackups that we use at Royal Circuits for a .062 board needing 1 oz of copper.
These might be our standard builds, but it is routine to change it and usually there is no additional charge for changing material thickness. For jobs that have impedance requirements we have the full suite of software that shows all the material used in your PCB along with the calculated impedances. It will also create a TDR coupon specific for your design that we can test to verify that the finished product matches the calculations.
There are lots of designs that the layer to layer spacing is important - including high speed designs, internal capacitance may be a factor, and different RF. You can work with us so it can be fully specified on the print prior to placing the order and that way future revisions will be built the same way.