That would very much depend on which 400 film, as well as which developer you'd be using. As an example, Tri-X in Microphen (a slightly speed increasing developer) can push much farther, than, say, APX400 in Rodinal (APX400 never pushed as well (as Tri-X) and Rodinal is slightly speed decreasing).
As Pablito says, it all depends on what you find accpetable. You can push Tri-X really hard and end up with some kind of image. Except for those who like the gritty black-and-white-and-nothing-much-else extreme push look, it maybe won't be of much use.
In the end, trying it yourself is the only way to find out. I'd recommend, as above, Tri-X in (Ilford) Microphen to start out. Others will perhaps recommend some different combination.