Start with the reference list, not the spend
Most multi-site operations carry more part references than they need, because each site solved the same problem independently. Rationalising references usually delivers more than negotiating price.
Availability is the acceptance criterion
Sites will comply with a consolidated channel for exactly as long as it gets them parts faster than the route they used before. Stock profile design is therefore part of the programme, not an afterthought.
Keep an escape route
There will be genuine emergencies. A defined process for urgent local purchase, with reporting rather than prohibition, prevents workarounds becoming permanent.