On EMT services, their form of GroupSave is available where Off-Peak Days Returns exist. They don't exist Bedford - Leicester: EMT think it's too far.
They do exist between Bedford and all intermediate stations (Wellingborough, Kettering and Market Harborough), and also between each of those stations and Leicester. One option is to buy two sets of tickets, for example:
BEDFORD STATIONS - MARKET HARBORO route ANY PERMITTED GroupSave Day 4 (GR4) £32.40. Restriction B1.
MARKET HARBORO - LEICESTER route ANY PERMITTED GroupSave Day 4 (GR4) £18.20. Restriction B1.
Total (for 4 people) £50.60.
But this combination is valid only by trains which stop at the station where you change from using one ticket to using the other. You can't use non-stop Bedford - Leicester trains.