Myxoinflammatory fibroblastic sarcoma (MIFS) is a rare low-grade sarcoma that most often involves the distal extremities of adults. Some MIFSs have been reported to show TGFBR3 and MGEA5 rearrangements. TGFBR3 and MGEA5 rearrangements have also been reported in hemosiderotic fibrolipomatous tumor (HFLT), in pleomorphic hyalinizing angiectatic tumor (PHAT), and in rare tumors allegedly showing features of both HFLT and MIFS (hybrid HFLT-MIFS). These findings have led to speculation that HFLT, MIFS, PHAT, and hybrid HFLT-MIFS are closely related; however, areas resembling HFLTs are only very rarely encountered in previous series of MIFSs. We studied classic examples of these tumors with the goal of clarifying the relationship between MIFS and HFLT-MIFS. Cases of MIFS (n = 31), hybrid HFLT-MIFS (n = 8), PHAT (n = 2), HFLT (n = 1), and undifferentiated pleomorphic sarcoma (n = 4) were retrieved from our archives, and the diagnoses were verified by 5 soft tissue pathologists. Using previously validated break-apart fluorescence in situ hybridization probes, we analyzed for TGFBR3 and MGEA5 rearrangements. Only 2 of 31 MIFSs harbored MGEA5 rearrangements; all lacked TGFBR3 rearrangements. Six of 8 hybrid HFLT-MIFSs harbored rearrangements of TGFBR3 and/or MGEA5. Both PHATs were positive for rearrangements of TGFBR3 and/or MGEA5. The HFLT was positive for rearrangements of both TGFBR3 and MGEA5. All undifferentiated pleomorphic sarcomas with focal myxoid change were negative. We conclude that (1) TGFBR3 and/or MGEA5 rearrangements are much more common in hybrid HFLT-MIFSs than in classic MIFSs, (2) HFLTs and MIFSs may be unrelated lesions, and (3) hybrid HFLT-MIFSs most likely represent HFLTs with sarcomatous progression, rather than tumors strictly related to classic MIFSs.