TARDISes are grown, not built. We don't know whether the metacrisis 10th Doctor ("Ten Two") would be able to grow one.
- That's not entirely true, as "the Doctor's Wife" shows the Doctor is able to build a rudimentary TARDIS from pieces of other TARDISes. So in theory Ten Two could do the same (as he possesses the Ten One's knowledge), if he were to ever stumble across a TARDIS or pieces of one.
- However, the junk TARDIS from "the Doctor's Wife" was hardly fit for long-term spacetime travel and, given the absence of a Doctor (and presumably all other Time Lords) in that universe, the chances of finding TARDIS scraps are extremely unlikely. Additionally, the junk TARDIS needed to be "jump started" by Idris before it could work.
Above - Also remember that Ten One gave Ten Two a piece of the TARDIS and Doctor-Donna told Ten Two how to accelerate its' growth so it could be grown within a few years. This was in a scene cut from the end of "Journey's End", but was included as an extra on the DVD. Russel T Davies said that he considered it to have happened, and they only cut it for length reasons.