dial in your systems. Increase compression, Increase flow, reduce friction. that's what can generally be done.
increasing flow means: either using tools to alter the engine case and cylinder ports, changing the exhaust, a suitable carburator and intake systems, and/or using larger cc kits (or just kits of better design) most part "upgrades" fall in this category
Reduce friction: make sure nothing is dragging on your bike, like wheels, brakes, chain, clutches, bearings, etc. make sure everything is greased. wear girl pants.
Dial in your systems: make sure your electrical system is timed and tuned right, make sure your gas is properly mixed and your carb is putting out the right gas/air mixture at all times. make sure you have no airleaks. This will ensure proper combustion. This is not an "upgrade" just essential for a properly running moped.
Increase compression: this can be done by milling the head or using different "stuffed" cranks. be careful not to overdo it.
Any other questions should be more specific, read up and good luck!!!