Split mash and combine for boil?

Here's a thought for the hive mind to dissect:

Mashes at higher temps yield a thinner bodied but more fermentable wort (forgive me if I get these backwards) while mashes at lower temps yield a more full bodied but less fermentable wort. Would splitting the mash into two halves yield the best of both worlds? I ask because I have two burners on my stove capable of boiling 3 gallons and two 4 gallon kettles . Was pondering a split AG recipe to combine later. Ideally I could mash in the two kettles and boil in a third larger kettle but....that larger kettle has yet to make it home to my equipment stash .

It is the other way around, but as to your question, I don't see how it would accomplish anything that mashing at a middle temperature wouldn't accomplish. I could be wrong, so hopefully someone more knowledgeable will chime in, but I don't think it would be worth it.