In this paper, the problem of mining high utility time interval sequential patterns with multiple utility thresholds in a distributed environment is considered. Mining high utility sequential patterns (HUSP) is an emerging issue and the existing HUSP algorithms can mine the order of items and they do not consider the time interval between the successive items. In real-world applications, time interval patterns provide more useful information than the conventional HUSPs. Recently, we proposed distributed high utility time interval sequential pattern mining (DHUTISP) algorithm using MapReduce in support of the BigData environment. The algorithm has been designed considering a single minimum utility threshold. It is not convincing to use the same utility threshold for all the items in the sequence, which means that all the items are given the same importance. Hence, in this paper, a new distributed framework is proposed to efficiently mine high utility time interval sequential patterns with multiple minimum utility thresholds (DHUTISP-MMU) using the MapReduce approach. The experimental results show that the proposed approach can efficiently mine HUTISPs with multiple minimum utility thresholds.