When I was initially a manager of a world wide, cross-corporate project, meetings consumed all available time on my calendar. I was still evaluated as an I/C so I would do my "I/C" stuff at nights and on weekends. This was unsustainable. Over time (I'd say 14-18 months) I convinced my management to either judge me as an I/C and replace my corporate role with someone else, or let me bring on someone (call the role whatever you want, lieutenant, Chief of Staff, whatever) who picked up my I/C work. I still did "I/C" work but as a peer to the guy I brought on board. For meetings I restricted who could add me to a meeting to about 100 people across the company. Anyone else had to go through an office assistant we had who'd vet the request and run it by both me and my lieutenant.
The other thing I did, even with those restrictions in place, was to narrow down the time window anyone could schedule a meeting to be no more than four hours a day. If it was critical to the business they'd call me or someone around me and we'd work it out, but that restriction wiped out a lot of stupid meetings that I really did not need to be in.
Put another way: put a visible price on your time, and really push back if there isn't a clear reason for you to be in the meeting.