It all depends on the anti-wear additive package chemistry of the oils, most oils (generally) do not have competing additives; some do/can have dissimilar additive chemistry. The only true way to know is oil analysis and looking at wear metals/chemistry from said analysis. The question I keep asking myself is but....WHY? Generally with information I can find online and analysis on virgin oil from projectfarm (does mostly objective side by side testing) , fordbossme (posts virgin blackstone analysis), and the motor oil geek (a chemist) youtube channels.
Pennzoil products (primarily Ultra Platinum/normal Platinum) seem to seem to be slightly above to above the average and Mobil 1/Castol is average at best based on published testing/analysis. That doesn't mean Mobil/Castrol are bad products, if they work for you based on mostly objective data, great.
The only true way to get consistent analysis oil an oil is run it at least twice in a row (2 changes) and do analysis on the second change when swapping brands. The first change is not a virgin analysis as some additives are adhere to the metal and residual oil in the sump (in these motors 1/4 to 1/5 of a court if you drain the pan, a little more than a 1/3 quart ish if you do a topside change) from the previous brand change.
What you also have to consider is oil companies change additive pack blends sometimes every year or two, so even though the package is identical you could possibly be getting a different overall forumlation. Mobil 1s 0w-40 from 3-4 years ago is not the same 0w-40 on sale at Wally World today, is one better than the other, from what objective measurement?
If the use the same additives in relatively the same % percent +/- 10/15 percent, the motor isn't going to care, and probably neither is the oil analysis going to show any changes of note, but is saving 5-10 bucks on an oil really worth all the effort, IMO to me it isn't.
Overall in general in additive packs in the last 4-5 years Calcium has been decreased from 1600ish down to 1100 ish to combat Low speed pre-ignition and Zinc has been decreased for emission system life as low tension oil control rings has become the standard to drop pumping loses and leading cars in general to use more oil, so more additive pack chemicals are being burned via combustion. Manufactures say 1 quart 3 quarts over an oil interval is ok....
. I roll my eyes, when I hear that bullshit.
The manufacturer of a vehicle is only interested in the warranty period ie...5 to 6 years where THEY are on the hook, so they have determined the car in general will "survive" have that time period with 6 oil changes. They have zero interest passed the warranty period, they give zero Fs and want to sell you a new vehicle.
"Lifetime..." fluids (ie coolant, trans, diffs) is market wank-i-teering for the warranty period...So if a service advisor or anyone at a stealer-ship says that (it's, "LIFETIME"), it needs changed every 50-60K miles. What condition will it be in with 60K miles and minimum "recommended" oil changes, probably starting to show some signs of using oil, depending on how it was driven.
Generally people only keep a car 3-5 years then they ("upgrade..."), to a new one. I try not generally to play F, (because I, "saved", 200 to 300 bucks over 3-4 years, etc..) the next guy, and it keeps the vehicle in good condition. Keeping the same vechicle on the road for longer is better for the consumer market, whether you keep it or it goes to the next guy, more availabity/greater number in the used market is lower prices for everyone, keeping prices lower.
Generally under normal driving, you could change the brand every time, as long as the weight/spec is on the bottle and the car will run fine. Can you possibly have a little more wear from change to change (seems to be what data indicates....), than sticking with one brand over the lifetime you have the car. Probably, indicated by testing. Is that small amount of wear going to reduce engine life, probably not significantly. But from the vechiles I have owned, majority indicate burning a signifant amoun of oil around 80-100K miles (noticable change on the dipstick), and the ones that do/have it's less than 1/3 a quart an oil change by measuring what came out and the amount going in around 100K miles. And generally the ones burning the oil are the used ones that I have bought used in the 40 to 80K range.