The term 'invade in great numbers' can be summarized by two crossword solutions: INFEST (6 letters) and OVERRUN (7 letters). INFEST means to inhabit or OVERRUN a place in large numbers, usually referring to pests or animals. OVERRUN is similar to INFEST, but it is more commonly used to describe an invasion of people or military forces. Both words imply a large number of people or creatures entering a place, often with the intention of taking control.