Certainly possible:

If in plastic, particularly PMMA, requires some lengthy fixation and 
processing.  The only limiting factor I can see is the way you would
cut the sections.  Large slab sections, ground to 100 um or so,
is very possible, for surface staining, would be beautiful, have seen
a whole dog leg (yes, whole leg, folks!) done in PMMA, a mouse is much
smaller, but the leg was ultramilled. Saws and grinders are needed here 
For PMMA sectioning, would require a microtome capable of cutting PMMA, 
tungsten carbide knives.  Polycut S or E comes to mind here, I am not sure 
even a 2066 Leica variety would be adequate, depends on age/size of mouse.

For paraffin, a piece of cake. Longer fixation, decalcification in
formic acid (15% aq), with xray endpoint checks if possible, good rinse
in tap water, then extended processing to  paraffin, could use up to
3 hours per station, infiltrate and embed in Tissue Prep 2, harder
paraffin, then section on a regular microtome as long as you have
good clearance on blade for the section.  A sliding microtome would
be very easy.  Have done whole mouse heads and whole rat heads, 
NBF fixed, decalcified with control, in paraffin, cut with high
profile Accuedge after a longer processing on a regular
microtome.  Was not difficult at all.  Removal of skin is advisable,
to get rid of hair and improve fixation, unless the fore and hindlimbs
or ears are part of the scheme.  Have an H&E migsagittal section of mouse
head, with upper and lower jaws intact, brain, eyes, etc. looking for
a special structure in nasal passages, which was found, a fun project.

Curious what this person wants to see in whole body sections, for IHC, 
the longer fixation would be better served with whole body perfusion,
immersion would be too long.  

Just some thoughts, actually always wanted to do a whole mouse,
might have to give it a try, certainly an interesting challenge.

Gayle Callis