After looking at several hundred linen drapers in the past, I'd never say rule someone out for 3 occupations, as it seems to be not all that unusual. Masters often appear to give their credentials under their livery company status but actual occupations can often appear as one or two unrelated crafts / occupations. (ie: our Fishmongers who were clothworkers?)
Have no idea if related, but as an example:
This John Wm Tongue....who acquired his own freedom in 1823, somehow deserved a knighthood somewhere betw 1848/1853
Began as an Undertaker, then Carpenter & Undertaker, then Undertaker & Boxmaker
70 & 71 North St John Street Smithfield, Msex - always as a Master Co Clothworker
!!! 1768 -William Tong "Master -Citizen and glazier, Co Draper"
Occupation "plumber" - "Strand near the new church", Middlesex
1715 William Tonge new apprentice father James
William Tonge New freeman Co Draper - father James Tonge woollendraper - maidstone Kent
1729 William Tonge -Occupation not stated - MasterCo Draper
1739 a Wm Tong witnesses as Wm. Tong Co Draper
1781 James Tonge New Draper's apprentice -father James Tonge grocer - Sittingbourne Kent, Kent
started out with William Field "cheesemonger" - Thames Street, London "Master Co Draper"
ended up with George "Harris" - "haberdasher" - Fleet Street S Brides, London "master Citizen & weaver"
( at freedom master Harris listed as Citizen & weaver Co Draper - Chatham Kent, Kent)
More under Tong Tonge Tongue
http://www.londonroll.org/Too early to be that Henry Todd, the draper, but will add as another example of oddities...
Henry Todd- father Christopher Todd of Durham -New apprentice 1704 who did well over his req'd time (freedom 1717) Christopher Doeker - "bellmonger" - Barnby Street Southwark, Surrey Master Co Draper