I think if the difference in size is big enough, you can combine almost anything. But I don't think the aesthetic of these typefaces work well together. I think Chaparral could be nice, it is a friendly and warm face, but avant garde is cold and stylized, and it is too geometric (in a bad way). If you like a geometric face, try Futura, Avenir or Neuzeit.

I just thought of Semplicità, but I'm not sure if it and Chaparral will ever share wine and cakes.

I would never combine Avant Garde with anything else.

As long as all your titles spell out Avant Garde you should be safe.

I second the idea of trying Chaparral with Avenir instead of Avant Garde.

Avant Garde seems like an odd choice to pair with Chaparral. I once used Chaparral with Today Sans and they looked good together, both "warmth" and informal typefaces in my opinion; the "headline" cut of Today Sans should fit well if it must be set for titling. I'd also suggest Nick Shinn's Sensibility as a compaion sans.

Hi, thank you al so much for your comments!
I was kinda hoping to get email updates on replies, but I didn't. Will check that in a bit. Sorry for the late reply.

I'm stuck with the Avant Garde because someone else designed the identity with it (and yes I have mentioned the phrase "Avant Garde only looks good when it spells Avant Garde" ;o)

But well.. I'm not allowed to change that, too bad.
Thanks for the help anyways!