She may be reading a history book = now; as we speak or these days; in the process of reading.
She may read a history book (no 'be') = sometimes; in the future; at an unspecified time (She may read a book every time she rides the bus; she may read a book tomorrow).
Yipes! My mistake-- confused by my own language! I thought we were discussing present tenses, and I thought read was pronounced /ri:d/ in your question. OK, in addition to my previous post; I will start again:
She may be reading a history book -- Yes, she herself is perhaps reading; as I wrote before: now; as we speak or these days; in the process of reading.