'Pushing' means different things to different people; the only common denominator is 'rating it faster than the box ISO speed'. Note that Delta 3200 and TMZ are NOT marked as ISO speeds, but as EIs or exposure indices.
There is no film on the market today which will not reach or exceed its box ISO speed in at least some developers, except perhaps Neopan 1600 where (unless they have changed it) they actually claim ISO 1600. Many films will exceed their box speed by up to almost 1 stop in the right developer -- typically Ilford Microphen or Ilford DDX.
These are true ISO speeds: speed point 0.10 above film base plus fog, ISO contrast.
A very few films will only deliver their true ISO speed in speed increasing developer. The most egregious example I know is Fomapan T200, which is about ISO 180-190 in Microphen. ISO standards allow speed variations of +/- 1/3 stop, so anything above 160 can legitimately be claimed as ISO 100. Thus, for example,
in the same developer, at ISO contrast, Acros 100 is likely to be 1/3 stop slower than Delta 100 -- but in (say) Microphen, Acros could legitimately be claimed (just) as an ISO 125 film.
By the same token, many films are much slower than their box speed in fine-grain or otherwise unsuitable developers. An ISO 400 film might be close enough to ISO 800 in Microphen, but ISO 250 or less in Perceptol: less than one-third of the speed.
Next, you need to know about long-toe and short-toe films. The easiest place to find out about these is probably:
http://www.rogerandfrances.com/photoschool/ps neg density.html (density and d/log e curves)
With a 'short toe' film, contrast builds very quickly with increasing development; with a 'long toe' film such as Delta 3200 or TMZ, contrast builds more slowly, so you can often get acceptable contrast even with extended development times. True maximum ISO speeds of popular long-toe films in typical speed-increasing developers are approximately 650-800 (Ilford HP5+, Neopan 1600, probably Tri-X but I don't know), 800-1000 (TMZ), 1000-1200 (Delta 3200).
So: true ISO speed depends on crystal habit, coating weight, type of sensitization and choice of developer. Acceptable 'push' speeds depend on subject matter, the contrast of your camera lens and enlarger lens, and personal taste. Remember, 0.10 over fb+f does not represent the minimum printable density: that can be as little as 0.03.
As a general rule, a stop or at most a stop and a half over true ISO speed can be surprisingly acceptable, but sooner or later you run out of shadow detail and contrast becomes too high.
In other words, yes, film can be 'pushed' to a higher true ISO than the box speed, though I regard this as a true speed increase rather than a push. You can then underexpose to varying degrees, and overdevelop to varying degrees, which I regard as true 'pushing', i.e. with increasing loss of shadow detail. At first the loss of shadow detail may be irrelevant, but sooner or later -- half a stop or at most a stop -- you have to kiss more and more shadow detail goodbye.
If only the mid-tones are important, as already noted, you can rate films incredibly fast -- Delta 3200 at EI 10,000 and more - but you will have no shadow detail at all.
You may also find the following useful on the subject of ISO speeds:
http://www.rogerandfrances.com/photoschool/ps iso speeds.html
Cheers,
Roger