MM IB to Distressed/SSG Possible?

I'm at a top MM IB in a top group. I really want to work at a firm that is able to invest with sizable checks across a capital structure. I'm fine with not working at Oaktree, Apollo, or Elliott, but find this kind of investing incredibly interesting. Is the move possible from MM IB, or should I attempt to lateral to a top BB/EB first to get a better brand name? I've read up a lot on the concepts and work done in distressed investing, but am not as familiar with the various funds and how they hire. Recently spoke with someone at a fund I'd love to work for and was told I would probably need a bank with a higher pedigree, so want to figure out if this is applicable to the whole field.