The top ones can - like Barenboim, Argerich, Lebeque sisters etc. Zimmerman travels with his own in his van, and has multiple keyboards set up to change the way his piano plays, depending on what he's playing - takes his own technician with him as well.
We've a really interesting DVD (Pianomania, soundtrack's in German sadly, although parts are English where people like Lang Lang are being filmed) documenting/following Steinway's top technician in Vienna Stefan Knuepfer, as he helps Alfred Brendel and others by selecting the pianos and setting them up. A lot of the DVD was spent in selecting and setting up a piano to match the concert hall where a Bach recording was to be made by Pierre-Laurent Aimard - and the work involved keeping the piano absolutely right during the recording. Names escape me, but part of the DVD was an accompanist being told that a partcular piano that the accompanist wanted was reserved for Brendel. And the accompanist had to use a house piano, albeit a perfectly maintained steinway concert grand. More info here:
http://en.wikipedia.org/wiki/Pianomania
- highly recommended if you can understand German, but no English subtitles...
But most just have to play what's in the hall - including talented players entering prestigious competitions.