Kodak recommends the same development times for 2TMY (TMAX400, gen. 2) at EI400 and 800, and both Kodak's densitometry [
Kodak 2TMY data sheet PDF] and other published densitometry indicates a true 400+ speed for the emulsion.
Of course, your rating depends on (1) how you personally meter; (2) how you develop; (3) what you'll do with the negatives. See
here for a more detailed view.
For me, metering reflectively with an M6 with recently-verified shutter speeds, XTOL 1:1 and EI400 work well, and if I underexpose by a stop I usually still get a usable neg. This is consistent with the above-linked Kodak PDF, which states that "no increase in development is needed for a 1-stop push."
As a side note, I strongly suspect that many photographers who use handheld meters see a lower effective speed for all materials across the board
not because film manufacturers over-rate their films, but rather because lens manufacturers don't provide T-stops for lenses intended for still photography. Cinematographers, of course, work to more stringent exposure standards, so they get lenses with labeled T-stops.
TTL metering compensates for the rather typical 1/4-1/2 stop difference between labeled f/ stops and actual light transmission. Handheld meters don't compensate for this difference. Anyway, that's my suspicion.
Edited to add: Oh, one other thing. The sensitivity curve of 2TMY is more red-shifted than the original TMY. I often use a yellow-orange filter (B+W 040), and I find that I'm using a filter factor closer to 3 than the nominal factor 4 that's recommended by B+W.
