The closeness to the wall behind certainly boosts any speaker's bass loudness, as I am sure you know. And many speakers are designed with midrange and highs much louder than their bass output, because they 'are designed' for that wall to boost their bass.
However, as soon as you choose to play it loud, what will upset you the most are the reflections coming off the wall all around the speaker cabinet, followed not too far behind by the reflections from all other walls and perhaps your floor.
If you absorb sound in the main voice range (middle of the piano), behind the speakers, it makes a huge difference in how you enjoy your tunes.
We recommend at least one 24 x 48 inch, 2" thick mineral-fiber panel, cloth covered, hung sideways behind each speaker, even though you said nothing can be done about your environment, acoustically. The ones from Auralex are nice, as well as those from Acoustics First.
FYI, the next reflections to treat, besides those from a bare floor, would be those off the sidewalls' points of first reflection.
Adding furniture helps to break up longer-term echoes, of course.
Good luck!
Roy