They did exist - by default of Network Southeast planning to keep 4 x 4-REPs after the 442 units were introduced. These were four units that didn't have asbestos. However, one was written off in the Clapham accident. The trailers were replaced with ex-TC trailers, so the loss of the buffet made them 431s (albeit still called a 4-REP) and numbered 1901-1903.
The plan changed again and they were reformed as 6-REPs, with only one DMSO (motor coach) located in the middle of the formation, with 4-TC DTSOs, 2 x 4-TCs TFKs and a 4-TC TBSK. They were then to be used, if I recall, on the Waterloo - Portsmouth via Eastleigh services after the line from Eastleigh to Portcreek Junction was electrified by NSE under the Solent Link scheme, that also saw the St Denys - Fareham line electrified.
With the recession in the early 1990s NSE had a surplus of units and as a micro-fleet the remaining REPs were withdrawn.
I have a recollection that NSE did consider an add-on order for an additional 4 x 442 units (that would have given a fleet of 28 units), which would have utilised traction motors from the remaining units. Not sure why that never went ahead.
I remember those 6-REPs being used on peak-hour (only) Portsmouth via Eastleigh services around 1990-91.
The regular hourly daytime service (similar in calling pattern to the current service, right up to missing Clapham Junction) was formed using mostly CIGs with the occasional VEP in 1990 (possibly interworking with the SOU-Portsmouth stoppers, though can't remember for certain), and purely Greyhound CIGs in 1991 (self-contained largely, with a CJ stop added) - but there were a couple of peak services (one of which divided at Eastleigh, half going to Bournemouth IIRC) formed of either 1x or 2x6REP. 1728 and 1758 or thereabouts out of London, IIRC. Those were, I think, the last through services towards Fareham out of Waterloo of the day, after that the service became Eastleigh-Portsmouth only as it was pre-electrification.
Back to the REPs, I travelled in either a REP or TC once only, in 1986 on the 'Network Day' between Brockenhurst and Woking on a 92, so not especially fast.
I do remember the '91's coming through Woking at an amazing speed though, at the time these were the only services to miss Woking off-peak, though the peak had some oddities, such as, IIRC, a string of VEPs going fast to Farnborough and then all stations to Eastleigh.
Almost invariably, at all seasons (my first experience of seeing them was in February), a REP + 2x4TC, I don't remember many, if any, REP + 1x4TC workings.
The '91's interworked with the '92's, a '91' up becoming a '92' down at Waterloo and vice-versa. Oddly, the '91' and '92' left Waterloo very close to each other, xx32 and xx45 - so not a very even service. In early 442 days this became IIRC a more friendly xx30 and xx50.
SOU to Waterloo in under an hour counting a signal stop - that is amazing, though achievable with a 90mph mean speed. If only we could achieve that these days; I do think there is an argument for a slightly-less-frequent off peak pattern on some routes but with more trains at maximum length to compensate.