If you have room, make and fit a Rear Toolpost. It will make parting off, with the tool inverted, so much easier.
I had enough room, so made a Four Way, to match the front post. It carries Front, and Back chamfering tools, as well as the parting tool. (HSS given to me when I bought my first lathe, back in the late 70s, and still not worn out! )
Admittedly, my lathe is larger than most, 1.5 hp VFD, 6" centre height, with 3" square toolposts, but have never taken more than 0.15" cuts. Not seen any problems with rigidity. But depends upon the design of the particular machine.
Howard