Here is my collection of the better 240s of Grandsire Doubles that each contain every change once at handstroke and once at back. The touches are listed as a set of leads with calls - bob (b), single (s), extreme (e), bingles (g) along with plain leads (p).

There are only three possible callings meeting the criteria just using the conventional calls:

pssbsspbpssspssbsspbpsss
pbppbpsbsppspbppbpsbspps
sssbssspsssbssspsssbsssp

The first two were created by Brian Price, while the third is credited to Leslie W.G. Morris. They can be rotated to give 32 touches.

We can produce additional callings of the better 240s by adding extra calls. Grandsire with extremes gives us a further 34 callings, or 1724 additional touches with rotations.

Now for the better 240s including bingles but without extremes. We have a choice of 79 callings falling into this group, which rotate to give 1692 additional touches.

Using bingles and extremes we have a massive 1574 callings or 36636 touches, of which 246 callings (5760 touches) contain all of the calls along with at least one plain lead.