School-wide app or software to collate homework assignments

Here's my problem:

I have 10-20 high school students assigned at the end of the day to me for resource time. (Most other teachers do, too.) Of course, most of them tell me (and other resource teachers), "I did all of my homework." Yeah, right.

I can spend my entire time with them messaging/emailing the 7 teachers x 10 students (or 20)...and have no time to communicate with/tutor/ride herd on my charges. (I have students with one or more D/F grade.)

I am looking for some software/online app that would allow the various teachers to record a brief assignment and then magically collate them for me by student. Does anyone know of such a tool?