bocadillo
Water Gypsy
It depends on the route.
You could go via Cross Country Trains if you change at Birmingham, or Virgin if you change at Nuneaton. But I'm not sure if they offer discounts on their own tickets, so you may find it's just as cheap to get them through East Midlands Trains. EMT could be cheaper if you go via Sheffield.
It could also be cheaper to split the journey into separate tickets, but that depends on the date(s) and times of your journey.
EMT offer a reduction on their own Advance tickets if you book them on the EMT website.