During our walk through I asked the technician where to set the jack. He said on the frame. The axle tube might bend or deform.
I have had two flats on my TT, both were nail like punctures. Having the proper cribbing wood blocks for the jack and having practiced before hand was the difference between a twenty minute delay and waiting for road service to find you on some back road.
As already mentioned, some folk jack on the center shackle but the tech said he told folk to use the frame, because it was the least complicated for most folks.
We now have a Tire-Aid but it too has drawbacks. On the sandlot I call a yard, I place it on a 2x8 board to keep if from being pushed into the ground. Also, some TTs have wider spacing between the wheels. I do not know how well it would work with a triple axle TT either.
I can say it is really handy when you want to adjust the brakes. Just lift one wheel and adjust the other.
Another thing to note is, just because you torqued your lug nuts to the specified ft./lbs. Does not mean they will be the same at your next stop. I find mine need to be tweaked twice before they all maintained the recommended torque poundage.
Good Luck