I was wondering what would happen if the two pumps weren't evenly matched? Would the oil accumulate on one side or the other? I guess it is pretty complex...
In the picture above, pretend that #5 (the oil filter) is actually a big oil tank with defoamers built in, and another oil pump built in that then sends the oil along to the engine via the same path it already follows in the current configuration.
If the existing oil pickup (#2) momentarily sucks air during a hard corner, then so what
since this pickup now feeds the oil tank. The new oil tank/pump that replaces #5 would be the one responsible for defoaming this oil, and then sending the foam/air free pressurized oil on to the engine.
The OEM oil pump would now be serving the role of a scavenge pump, collecting return oil from the engine and sending it to the new external tank, which would then be used to supply pressurize oil to the engine via a "new" pump from somewhere. Checking to see how the supercharger guys do it might give some ideas.