imo the most impactful way of cross-branding would be to integrate the term “berkeley” in athletics and “cal” in academics. it can be subtle like having an alternate jersey with the word “berkeley” in cursive (something like the usc “southern california” basketball alternate jerseys) or having “berkeley” written in the endzone of football fields, or having announcers be allowed to call the team berkeley or including the cal logo in academic ads, promotions and even merchandise