Systems and methods are provided for improving the processing of heavy or challenged feeds in a refinery based on integrated use of deasphalting, coking, and hydroprocessing. An optional fluid catalytic cracking unit can be included in the integrated system to allow for further improvements. The improved processing can be facilitated based on a process configuration where the vacuum resid fractions and/or other difficult fractions are deasphalted to generate a deasphalted oil and a deasphalter residue or rock fraction. The deasphalted oil can be passed into a hydroprocessing unit for further processing. The rock fraction can be used as the feed to a coking unit. Although deasphalter residue or rock is typically a feed with a high content of micro carbon residue, a high lift deasphalting process can allow a portion of the micro carbon residue in the initial feed to remain with the deasphalted oil. The portion of micro carbon residue that remains in the deasphalted oil can then be upgraded during hydroprocessing and/or during subsequent processing of the feed. By reducing the amount of micro carbon residue passed into a coker for a given initial feed source, the overall capacity for a reaction system to handle heavy feeds can be increased relative to the rate of coke production from the reaction system.