It's a matter of (a) prioritizing and (b) scheduling. If you believe going to
all those meetings is very important, then when people suggest at meetings
that you take on a task, you can say something like "No, I'm sorry, I won't
have time for that. I'm busy with meetings all day all the time."
If you believe that it's also good for all the other people at the meeting
to spend all their days at meetings, then you'll be setting a good example.
(And contrariwise if not).

If you believe that some actions are more important than some meetings,
then when people schedule meetings you can say something like
"No, I'm sorry, I'm going to miss the meeting this time in order to
get some stuff done ... I expect to be at the next meeting though."
If you believe it's good for the other participants at the meeting to
sometimes skip meetings in order to get stuff done, you'll be setting
a good example (and contrariwise if not).

You can do arbitrary scheduling, such as "On Tuesdays and Thursdays I
don't go to any meetings unless they're really, really important, and
generally a maximum of 2 hours of meetings a day even then. My Tuesdays
and Thursdays are primarily for non-meeting work. On Mondays,
Wednesdays and Fridays I go to lots of meetings." Or "I don't go
to any meetings between 12:00 and 14:00." Watch out for the "parkway"
phenomenon: cities saved up "greenspace" for parkland and nature,
and then ended up noticing that it was a convenient place to put
huge highways. How do you protect your action time from having
big important meetings pushed into it because people know you're
(in some sense) not busy then?

Each week you can list your meetings in order of priority and skip
the bottom few. If two meetings are scheduled at the same time
you probably know which one you'd go to; you can use the same
thinking process to list all your meetings in priority order, to limit the
number of hours per week of meetings.