Why are there sometimes multiple asol1.fits files for my observation?
How do I treat these in my analysis?

An aspect solution (asol) file is created for each stable aspect interval. There are many reasons why an interval could be broken, e.g. a gap could be created by a small section of bad engineering data. When a tool requires the aspect solution, all the files must be input, either as a list or as a stack (see ahelp stack for more information).

For instance, when running asphist, the aspect solution file is input to the infile parameter. As mentioned, this may be done as a stack:

unix% pset asphist infile="@pcad_asol1.lis"
unix% more pcad_asol1.lis 
pcadf057736899N004_asol1.fits
pcadf057763996N004_asol1.fits

or a list:

unix% pset asphist \
      infile="pcadf057736899N004_asol1.fits,pcadf057763996N004_asol1.fits"

The filenames are specific to your dataset; these are from ObsID 3.