After failing to qualify in his International Formula 3000 debut at Brands Hatch, and a brief foray in the United States' racing scene that included three starts in the new American Racing Series (current Indy NXT), Cheever switched his attention to Japan in 1987.
He narrowly lost the 1989 title to Hitoshi Ogawa by three points, and again in 1991 at the last race to Ukyo Katayama, finishing second both times.
After his first prototype experience in 1987, Cheever returned to a Toyota seat with Dome in 1989, which included a 24 Hour of Le Mans run that ended in an early retirement due to an engine failure.
In the summer of 1992, Cheever dovetailed his F3000 season with his Indy Car debut for A. J. Foyt Enterprises in 1992, racing against his brother Eddie.
He was entered in a second Cheever Racing car for the Indianapolis 500 and completed rookie orientation.