Welch owned Erdenheim Stud at Chestnut Hill, Pennsylvania. In 1870 he purchased the mare Maggie B. B. from Captain T. G. Moore and stood her at Erdenheim. In 1872 he purchased the sire Leamington. Welch's broodmare selections led to Leamington becoming the Leading sire in North America in 1875, 1877, 1879, and 1881. Among those bred to Leamington was Maggie B. B. who produced three Classic winners in all, two of which were sired by Leamington. Their first was the 1879 Preakness Stakes winner, Harold, and their second was Iroquois, who in 1881 became the first American-bred horse to ever win England's famous Epsom Derby. Maggie B. B.'s third Classic winner was the colt Panique by Welch's stallion, Alarm. Panique won the 1884 Belmont Stakes. 
Among Welch's clients was friend and fellow Lexington breeder, Hal Price McGrath, owner of McGrathiana Stud. McGrath's mare Sarong was one of Leamington's mates in his first season at stud for Aristides Welch, producing a colt which McGrath named Aristides in honor of his friend. The horse Aristides won the inaugural running of the Kentucky Derby.
In May 1882, Aristides Welch sold Erdenheim Stud and the bulk of its bloodstock to Commodore Norman Kittson and his brother James of Saint Paul, Minnesota.