Highest OG in a 10 gallon cooler

This might be obvious and unhelpful, but if you are doing a single infusion mash, couldn't you just mash 2 batches of grain?

 

All other things being equal (please re-read those first five words...no variables except for sparge type), Fly Sparging will yield higher efficiency than Batch Sparging. Think about the wort that is left behind in the mash tun, absorbed by the grains. The volume of this wort will be exactly the same, regardless of sparging method. But the 'left behind' wort from a batch sparge will be of a higher gravity than the left behind wort from a fly sparge, because it hasn't been continuously diluted as in the fly sparge. Sugars that are in the wort left behind in the mash tun are not in your kettle. It's that easy. All other things being equal, sparge efficiency works like this, in order of increasing efficiency....

No Sparge
Single Batch Sparge
Double Batch Sparge (uneven volumes)
Double Batch Sparge (even volumes)
Triple Batch Sparge
Fly Sparge

It's all about the gravity of the wort in the mash tun (in the grains) at that last moment when runoff ends.

Edit: although I know the above to be true, I usually do no-sparge, and occasionally single batch sparge.