It isn't implemented to allow both, no. There are a couple ways that
come to mind to address problems with having both, but as-is it would be
confusing - do you show the group heading if the grouping is split
between pages on both (or more) pages, or not (it wouldn't now)? You
probably should, but that could make it hard to comprehend. Do you show
the total count on both? Again, should, but that would also muddle
things. The biggest issue would be not being able to see the aggregate
grouping across all of the selected data, which is part of what the
grouping feature is for.
I imagine retooling the grouping implementation to recognize paging and
display a sensible split-page header (e.g., "Group 1 (21 through 40 of
55) on this page)" and show across split pages would make this more
feasible.
(Long answer in case someone feels like breaking out their hacker hat.)