you will make more buy selling the individual pieces and not selling it as a whole. Of course, that is more time and effort so you have to consider how valuable your time is to you and whether it is worth the effort. If you just want some reasonable money but don't need to maximize profit since your time is more valuable then sell it has a whole and keep the headset if you want.
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1 Super Record bike, 1 Nuovo Record bike, 1 Pista, 1 Road, 1 Cyclocross/Allrounder, 1 MTB, 1 Touring, 1 Fixed gear