It's nice to see that X-Rite has just released a public beta for software that allows custom camera profiles to be used in Capture One. I've been using one for Adobe software for years and it does make a small, but significant difference in final image quality.
If you have X-Rite's ColorChecker Passport or ColorChecker Classic you can have the same functionality that has been available for both Adobe Camera Raw and Lightroom users.
https://xritephoto.com/CameraICC?utm...0Capture%20One