A total of 136 horses go forward for June 4 showpiece at Epsom, up from 102 at the same stage 12 months ago.
Trained by John Gosden and owned by Highclere Thoroughbred Racing, Foundation won his first three starts last season before suffering trouble in running in the Racing Post Tropy at Doncaster.
Midterm is by 2001 Derby hero Galileo and the first foal of six-time Group One heroine Midday, narrowly beaten in the 2009 Oaks.
Owned by Khalid Abdullah, who has enjoyed success three times in the premier Classic, Midterm was the comfortable winner of a mile maiden at Newbury in October.
Racing manager Teddy Grimthorpe said: “At the moment he’s just a maiden winner and people can start getting excited when he’s achieved a bit more.
“There are no plans as yet.”
Aidan O’Brien has won three of the last four renewals of the Derby and five in total, and has more horses left in than any other trainer, with 36 contenders in total.
These include Racing Post Trophy runner-up and subsequent Criterium International winner Johannes Vermeer, impressive maiden winners Cook Islands and Idaho.
As well as the O’Brien-trained horses, owners Sue Magnier, Michael Tabor and Derrick Smith also have an interesting contender in the Gosden-trained Royal Artillery.