The Case 570 appears to be just a tractor
TractorData.com J.I. Case 57 tractor information
So it's likely that a 3PH for that tractor would be just the "normal" farm type, no power down, etc -
What model Case 580 you have would determine what you can/cannot do - not sure when the change happened, but somewhere around the C or D model ? the 580 was ONLY a backhoe, only way to take the hoe off was in PIECES -
I have a 580B, the hoe (and other attachments) mount on a 4-point subframe I also have the factory INDUSTRIAL 3 point attachment - no draft control, but DOES have TnT plus one remote, AND it has float AND power down but does NOT have position control. The Down valve is just a normal power up/down or FLOAT.
When I say "power down", I'm not kidding - with the 7' Gannon box on the back, I could easily lift the tractor's rear wheels off the ground...
If you get some experience (AND make a pair of 6' extender hoses) you can swap between hoe and 3PH in about 1/2 hour, but a couple of the mount components take 450 ft lbs of torque - I finally got tired of the swaps and bought a couple used tractors for regular implements. Also, even tho you might find a rear tranny plate with a PTO, it would need to COME OFF before the hoe goes back on (not enough clearance) - another reason I gave up on "one size fits all"...
Here's a pic (not mine) of one that's just like mine -
Again, a bit more info (model, what you wanna do) might help us help you... Steve