Are you considering modifying an existing turbine engine to have an additional compressor stage, or are you thinking of designing a completely new engine with a two stage compressor? Either way you are in for a lot more work than you seem to realize!!!
I am no expert on the subject, but I would guess that (with centrifigal compressors, which are what is used on every model turbine engine on the market today) the additional mass and complexity added to an engine in order to have a multiple stage compressor will almost certainly cancell out any performance gain you might achieve with such a setup.
Adding an additional centrifigal compressor stage to and engine would require considerable machining for internal ducting and would probably lengthen the engine by around 30%. The longer engine would require a longer main shaft which in turn would require more bearings to support it. This is assuming of course that you were able to get by with only a single shaft (i.e. both compressors driven by a single turbine wheel at the same rpm) which is doubtful. Using available compressors (automotive turbo wheels) it is more likely that in order to achieve maximum boost you would have to select compressors with different pitches and drive them at different rpm's which would then require multiple turbine wheels and multiple shafts, along with more than twice as many bearings, which will all require lubrication. You are 'as they say' building a boat in the basement!


As for your other concern, why does the starter mounted in front of the turbine cause you more concern for FOD? Are you worried about the starter motor itself coming apart?
If this is your concern then don't worry. In all of the designs I have seen there is very little chance that anything like this could happen. Two of the major manufacturers use an aluminum tripod mounted to the front cover that supports a machined aluminum "pod" that houses the starter motor. The legs of the tripod are either thick walled tubine with a bolt running down the center from inside the pod to the front cover, or they are threaded with a screw at each end. In either case if one or more of the leg securing bolts were to loosen and let go I doubt the remaining leg(s) would allow it to move enough to go into the compressor, and the hardware that came off of it would be captured inside of either the pod or the front cover, and it is likely that if one leg started to loosen you would have plenty of warning before it let go completely in that the engine wouldn't start because the starter was not able to engage the compressor spinner. The only other starter motor mounting design that I am aware of is what is used on the Jetcat engines. They use a one piece molded nylon mount/starter pod. It is one piece, and will not fit into the compressor. As far as I know there has never been a failure of either design during normal operations.
By far the most FOD that any model turbine will ever see is from insects, grass, sand, and gravel. The only FOD that has ever done any damage to my turbine was a bubble gum card sized candy wrapper that zipped into my intake during a full throttle run up on the ground.
The added complexity of gearing a starter from the side (or inside the front cover) would significantly add to cost fo producing an engine, and your concerns about a front mounted starter causing FOD are mostly invalid. There is no need to fix what is not broken.

Kevin Whitlow