Fred - reflecting on your comments that the lid for sugar box Rd. 321369 appears not to have been Registered at the same time as the base, seems unusual perhaps, and I've looked through the seven Nos. you indicate as possibly harbouring the Reg. for the lid only - Nos. 318789 to 318795. Regret to say I'm unable to find a Registration for said lid within the number range you mention, but what suddenly occurred to me is the fact that these seven Nos. were allocated something like 4 months prior to Registration of the base (May of that year). It appears rather back to front that a component such as a lid might be Registered months prior to its intended base - suppose you might argue that this lid served as a 'part' for more than one Registration - but we'd need proof of that suggestion, and I don't see evidence of that in the Kew drawings.
As you have pointed out, the base for this 'sugar box' appears in Sowerby pattern book XI, minus its lid - but it does appear in the factory drawing with the lid, which would have been the official information supplied by Sowerby to the Board of Trade. So do we argue that the data provided to the Board of Trade on the 14th of May 1878 i.e. the whole design including lid, should be our criteria for assuming that Reg. 321369 was indeed intended to cover both lid and box?
What in particular made you suggest that the lid might occur within the seven Registrations from 20th February (parcel 3) of that year?