It is certainly achievable in 3ds Max and i see no reason why it shoudn't be possible to do the same in C4D. Attaching screenshot of quick setup in Max, hopefully it's somewhat useful to help you to transfer it in Cinema. Short description - plug pure white Corona color shader into Corona tone map control, then into shadow catcher and then into ray switcher. Make sure that exposure, tone mapping and/or LUT are unchecked in tone map control shader and keep in mind that not all tone map control operators can be completely reversed, so you might need to adjust your tone mapping in the VFB if you're not getting pure white background. Ray swither is optional, but without it helps to get more natural illumination of your subject.
Keep in mind that shadow catcher is a special kind of material and how it reacts to shadowing is not very intuitive and possibly physically not very accurate. This is especially evident in edge cases like this, where the background colour is pure white. I wasn't able to get any shadows from HDRI, so had to use Corona lights to illuminate the scene and even with those some tinkering is necessary. In my example two side lights have enabled shadowcatcher illuminator, while the top light has it disabled. You can try different combos to see what works for you, but if all lights have this option either enabled or disabled, they will cast almost no shadows on the shadowcatcher. This limitation only present when background colour is pure white. If you're ok with darker background, then shadows should work just fine, even with HDRIs.
