Now I'm at home and have access to my reference books, I can be a bit more specific.
There is a detailed table of vehicle numbers, types etc in BR First Generation DMUs in Colour by Stuart Mackay (Ian Allen , published just before Christmas and should therefore be available in bookshops) . Those Who Know say that this book is very accurate and that some earlier books on DMUs have quite a lot of errors in captions etc
Anyway it confirms bangerblueed's comments - only 5 x 3 car units, delivered to NEReg in 1958. There were however 6 x 4 car units , also delivered to NEReg in 1958. These units had both driving cars powered. The 4 car sets had a Trailer brake second with lavatory, a TSL and 2 x Driving Motor Composites, the 3 car sets had Driving Motor Brake Second, DMCL, and TSL.
According to Golding's book (Pictorial Record of BR DMUs, Cheona 1995) the body of a DMCL and the body of a DTCL are the same and the same drawings in the book apply , the difference is below the underframe
In other words , Bachmann need 1 extra vehicle for the 3 car unit (TSL), plus a new underframe for the composite and having done the 3 car they can build up to the 4 car with one extra vehicle (TBSL). At that point I'd imagine they stuff the mechanism in the central TBSL and you're up for 3 decoders
108 power twins seem to have been an LMR speciality, at least in the first instance: 12 2 car power twin sets in 1959, and a further 29 in 1960, with roof mounted 4 digit headcode boxes
108 2 car power/trailer formations, as depicted by Bachmann , were the most common 21 sets for the NEReg + 5 for LMR in 1958, followed by another 59 sets for LMR in 1959-60. A final batch of 21 for the LMR in 1960 had roof headcode boxes
The reason for power twins was presumably that 108s had 2 x 150bhp Leyland engines , whereas some other DMUs had 230hp Albion engines. There were some fairly steeply graded bits of the LMR in Northern England and presumably it was quickly decided power twins would be needed in some places. I remember toiling up the Long Drag on a Leeds-Carlisle local in the mid 80s on what I think was a 108, and Aisgill was cleared at around 45mph from memory. I assume that must have been a power twin - I doubt a power trailer unit with 150hp engines would have been let loose on that. This was before the S&C was full of heavy coal trains with Type 5s on the front - I doubt the operators would let an elderly lowpowered DMU struggle up to Aisgill today
If anyone's wondering why the ER missed out on 108s, initially - they had already 49 x 2 car 114 Derby Heavyweights based at Lincoln : these were 8 tons heavier, power/trailer sets and soon got upgraded to 230hp Albion engines