You'd need an SDR dongle and a software-based decoder that:
a) decodes DMR
b) only requires one dongle to monitor a TIII system (depends on certain factors)
can either
c) understand and track a TIII system
-or-
d) scan channels without getting stuck on the control channel
Pretty sure that the free DSD+ 1.101 can handle a), b) and d) if an FMP scanlist is created with all RF channels specified as DMR channels; FMP should skip over the control channel unless the second timeslot is carrying a voice call. But that's for one of the cheapie SDR dongles - DSD+ 1.101 doesn't support SDRPlay SDRs.
DSD+ FL can handle a), b) and c) and would work with an SDRPlay RSP2.
I assume SDRTrunk and OP25 can handle a), c), as well as b) if the span of all of the system RF channels fit within the dongle's sampling rate (I don't imagine that 220 MHz system channels are spread across much spectrum, so b) should be a non-issue...); not sure if they support SDRPlay devices and specifically the RSP2, but I suspect that they do. Someone else will know for sure.