Do you have any suggestions concerning possible apps to try?
As ahull says, it would be easier to suggest if we had more information about the specifics. Tell us what you are trying to do, not just little pieces.
Some possibly relevant questions:
How many different kinds of cameras?
What kind of scenes are they shooting? If the scenes are diverse indoors, outdoors, different lighting, then the problem is more complex than if it's one kind of scene.
How many images?
How similar do the images need to be? Do have a way to measure whether they are close enough?
What software skills do you have available? If you have a programmer with a strong image processing background the answer will be different than if you only have people who are terrified by a command prompt.
Without knowing any of this my inclination would be to try to use something like raw therapee, because it understands raw files, has very flexible color adjustments, and is able to operate in batch mode. It seems like if you get (near) identical reference scenes, you should be able to manually come up with a profile that gives you similar results for each camera, and then use that to batch all the subsequent images. Obviously this wouldn't scale to large number of cameras.