I am currently working on designing an immunoadhesin construct bound to IgG Fc region. Most of the work I've seen so far removes both the CH1 and VH domain of an IgG while retaining the hinge and CH2-CH3 domain. What would the CH1 do if present?
The VH1/CH1 domain contains the antigen binding site. This would cause off target binding of your Fc-fusion protein if not removed. The CH2-CH3 domains are important for promoting/extending the plasma half-life of your fusion partner. That is why they are used. Fc receptor binding may occur as well.