Not much if you put it on a M37. 240 gallons of fresh water weighs right at 1 ton (2000 lbs). That's way more than what M37 is rated to handle. I don't think I would like to drive one carrying more than three loaded 55 gallon drums in the back which would be 165 Gal, getting close to the 3/4 ton rating and more than enough sloshing, unbaffled liquid moving around to make me nervous. 165 gallons really isn't that much water in terms of needing it for a job but it's a hell of a lot of weight for a truck to handle, especially one built in the 50s. When I worked at the Dodge dealership here in town, a local Volunteer Fire Dept brought in their '77 Dodge W300 dually mini pumper because the axle seals were leaking and no one could fix it. Turns out they had bent the D70 housing loading too much water in it fighting a brush fire. I don't know what the capacity of that truck was, but it wasn't anything large or extravagant. They refused to replace the housing a later snapped an axle shaft right at the flange and traded it to a chassis company for a Ford Super Duty mini pumper than I was told had a much smaller tank.
Another thought has crossed my mind and that is why you need a military truck for this? You seem to want to put a clear agricultural tank on the back, so it is not going to look military. You also say you don't have the cash for a Deuce tanker which the ex-fire trucks seem to sell on GSA for cheaper than you can buy a M37 off ebay most of the time. So why not just buy a civilian dually or 2 ton truck? Around here you can buy an old Ford F600 for next to nothing and it would definitely be a better platform for this project in my mind. Why cut up a piece of restorable military history to make something that is going to be inferior to cheaper and easier alternatives? Just my .02