All three English sides top their respective pools, with the Pirates - inaugural cup winners back in 2010 - best placed to book an early slot in the knockout phase.
The Duchy outfit holds a nine-point lead at the top of Pool 6 after a last-gasp 31-20 win over Jersey at the Mennaye Field maintained their perfect record.
Should they get a fourth bonus point win in the return match at St. Peter's this weekend, and Ayr fail to do likewise away to Ulster Ravens, Ian Davies' men will be mathematically certain of a place in the last-eight with two rounds to go.
Albion have a stiffer task on their hands despite making it three wins out of three with a 17-7 home win over 2012 champions Munster 'A'.
The Devon side a four-point lead over their Irish province at the top of Pool 4 going into the second part of their double-header, to be played in Waterford on Friday evening.
Bristol, meanwhile, appear to face a two-way tussle with Leeds Carnegie to finish top of Pool 5 after a record-breaking 78-0 win in Tuesday night's rearranged fixture against Aberavon put them two points clear of Carnegie.
Bristol scored 12 tries as they powered to the club's biggest ever win in cup history. They play their third game in six days when they take on Gala in the Scottish Borders this weekend.
Leeds, meanwhile, will hope to back up last Saturday's 41-22 success over Aberavon with a victory over the Wizards at Brantingham Park, the home of Hull Ionians. Leeds beat London Scottish 26-3 the last time they hosted an 'on the road' game there, in March this year.
Leeds' Yorkshire rivals Rotherham will fancy their chances of taking another step towards quarter-final qualification as they welcome Llanelli to Clifton Lane.
Following a 20-16 win over Llanelli in the first ever meeting between the sides, the Titans hold a narrow one-point lead over Connacht Eagles - who were impressive 17-8 winners over Bedford Blues in the last round - in the Pool 3 standings.
Lee Blackett's men have only lost once at home all season - to Championship league leaders London Welsh.
Cross Keys will need to produce a special performance to avenge a 31-0 loss at the hands of defending champions Leinster 'A' when the two sides meet again at Pandy Park on Saturday.
The defeat at Donnybrook ended a seven-game winning run for Cross Keys, who have not been beaten on home turf since losing to domestic league and cup champions Pontypridd on September 21. Leinster 'A' lead Pool 1 by four points.
Seasoned British & Irish Cup campaigners Pontypridd hold sway in Pool 2 following a 27-20 win over London Scottish, who they meet again this weekend. London Welsh travel to Edinburgh Academicals looking to back up last Saturday's 73-10 win at Old Deer Park.
BRITISH & IRISH CUP - ROUND 4 FIXTURES:
Friday, December 13 -
Munster 'A' v Plymouth Albion, Waterford Regional Sports Centre, 7.30pm
Ulster Ravens v Ayr, Deramore Park, 7.30pm
Ealing Trailfinders v Moseley, Vallis Way, 7.45pm
Nottingham Rugby v Stirling County, Meadow Lane, 8pm
Saturday, December 14 -
Edinburgh Academicals v London Welsh, Raeburn Place, 2pm
Bedford Blues v Connacht Eagles, Goldington Road, 2pm
Rotherham Titans v Llanelli, Clifton Lane, 2pm
Leeds Carnegie v Aberavon, Brantingham Park, 2pm
Cross Keys v Leinster 'A', Pandy Park, 3pm
London Scottish v Pontypridd, Athletic Ground, 3pm
Gala v Bristol, Netherdale, 3pm
Jersey v Cornish Pirates, St. Peter's, 3pm