Hi Anita,
Were you able to solve the problem, I'm currently working on geocoding addresses for accidents data as well, and they have (1)- "On" street, (2)- "At-between" street and (3)-"Between" street, which derived into incidents happened at (1) in between street (2) and (3).
I'm able to do intersection between (1) and (2), however, that would not be entirely accurate, since some incidents data have (3).
Let me know what do you think, thank you.
Amanda