Decomposition of the time reversal operator (DORT) was recently applied to the problem of detection and location of soft faults in wire networks and proved effectual when dealing with a single fault, even in the case of complex network configurations. In this paper, the case of location of multiple faults is addressed, first proving that the standard DORT formulation does not allow to take a clear decision about the individual position of each fault. An alternative version of the DORT, based on an updating procedure, is presented and demonstrated to enable accurate and selective location of multiple soft faults. The proposed procedure is also shown to allow estimating the reflection coefficient of each fault, thus giving access to their severity.