Yes you can do full boils. Yes you can do all grain.
Use a plastic bucket (bottling bucket or fermenter) to hold the runnings from the MLT.
Pour 3 or 3.5 gallons into the pot, boil it, cool it, add it to your fermenter, pitch the yeast. Then boil the rest, cool it, add it to the fermenter.
Just do it in two batches. It'll add 40 to 90 minutes to your brew day, depending on how quickly you can chill the wort and a few other factors.
Actually, since you can start boiling before you collect your sparge, maybe it wouldn't even take all that much longer....