Different framing for different objects

I'm working on a 2.5D game with a camera that has a fixed rotation.
So far I've been using Cinemachine to follow a TargetGroup, but this won't suffice any more.

What I want is to have my player character on screen at all times and another object on screen if possible with the camera moving / zooming within defined constraints. Most of this is fine, but naturally as the player moves away from the other object the TargetGroup position will be too far away from the player for the camera to keep the player in frame.
I have a higher weighting on the player, but I can obviously only push that so far, and the same applies with the max ortho size / cam distance.

What I would like to be able to do is define different framing settings for the player and the other object, and then the camera uses a sort of average / max of the two:

• The player should always be within shot (plus deadzone)
• The other object should be within shot if possible (max distance restraint)
• If the other object is not within shot, the camera shouldn't snap back to the player (for example I don't want to just remove it from the target group if it's too far away)
• Additionally I'm using some look ahead on the player

I don't see a way of defining something like this so I thought I'd ask before implementing our own solution.

Suggestions?

 

I think it will require a more manual solution as both of those options essentially amount to the same idea and neither of them quite work. For example, setting the weight to 0 for the other target would ignore it as you say which I never want, and finding the right weighting balance to update it live is fiddly.
Thanks for the suggestions though, Using the MixingCamera elsewhere and I really like it.