I looked at 3 CR 15 monsters. One was an agathion, and one was a a demon. Both had cmd of 41.
Strangely a Jotund Troll is huge, and he is only cmd 33.
But even with the Troll you need a pretty decent base bonus to have much chance at doing a maneuver with him.
Maybe +10 is too much. But I can tell you this stuff gets big fast the higher CR you get to. It takes a dedicated build and tricks to pull it off.
The dragons at CR 15 are like cmd 40, 41 things like that.
If you pull a maneuver on Joe Sorcerer he isn't going to resist any of your maneuvers probably without shapechange magic. So I really don't know what to say.
Wish someone who had played a grappler or something at high levels would give some input as to the bonus you need to get things done.
But all the explicitly high cr stuff has really good cmd unless they are mostly class level based.
Heck a Storm Giant is cr 13, and has cmd 42. It may seem unrealistic to some, but I kind of expect a 15th level monk (or other character) whose whole thing is wrestling to be able to grapple a Storm Giant and have decent chance to win.
And I have no particular reason for picking CR 15 to look at monsters. It's just higher than level 10, which to me is where things start to really wonk out.
Ah, crap was going to close the window I pulled up Storm Giant in, and saw the constant Freedom of Movement. So I guess no one is grappling a Storm Giant unless they are in an antimagic field or something. Forgot all about that FoM thing.