This is independent from anything else in "Improved X selections" so
I'm splitting it out - it just adds a customization
mouse-save-then-kill-copy-region that is pretty similar to
mouse-drag-copy-region, only for mouse-save-then-kill (mouse-3).
Attached patch implements desired feature.

mouse-save-then-kill is useful for (but not only for) its
region-adjusting features, since it allows the point and mark of an
active region to be moved separately with the mouse using its "who's
closest" algo, particularly handy when the point or mark is offscreen.
 But, like mouse-1 dragging with mouse-drag-copy-region non-nil, it
insta-saves.  It'd be nice if one could have mouse-1 and mouse-3
behaviour that fitted in together when mouse-drag-copy-region is nil.

The customization allows one to choose whether mouse-save-then-kill
has its original behaviour (adjusting the region and insta-saving, the
default), only region-adjusting, or  a "double" option that "saves"
save-then-kill functionality, so you can double/triple click instead
of single/double click for save/kill, but single clicks just adjust
the region.