Just catching up to an ole thresd here...
According to Griffith's "Operational Reference", Rescue Compnaies "are also assigned on boxes if closer than the first due ladder company"...
I am familiar with R3. In their previous quarters on 176th Street, R3 had a handful of boxes where they were closer than first due assigments for L's 27, 33, or 38 and they would go on the box. If any of those were closer, R3 would wait for a 10-75.
I have a older version of the OPS/REF so please advise if this policy has changed. Also, R3 has moved south of L27 on Washington Avenue so if still in effect it would now affect L's27, 19, and maybe 31 and 44. STARFIRE, however, seems to still have R3 responding 1st due on the box to their old assignments vicinity Tremont/Burnside Aves. Perhaps a little re-programming is in order?