Long ago (well within my lifetime), it was a very very very bad idea to mix oils of two different BRANDS together - like it's filled with Havoline, ya top it up with Quaker State, bad stuff happens. Today's oils are very different from yesterday's oils, but still I get tense about mixing two different brands. No problem with a different viscosity oil, but I don't like to mix brands.
At an oil change, I may switch brands... na, I don't even do that - I've been using Pennzoil since the late 1970s. It may be time for me to look around, though, & maybe switch to Rotalla for the CJs.