1
general::
Encroach on, advance at another's expense, as in The Japanese rapidly made inroads into the computer-chip market. The noun inroad originally meant "an invasion." [Late 1600s]
American Heritage Idioms
2
general::
Phrase(s): make inroads into something
Fig. to succeed in getting something done or at least started. • George was unable to make inroads into solving the problem. • We are making no inroads into the high-priority project.
McGrawhill's American Idioms And Phrasal Verbs