All that kind of thing gets really murky in a band context. I don't want to derail this and go too far off on a tangent, especially given the actual subject matter of the thread, as I don't want to distract from that. But since this has come up a few times, here's a bit of insight:
[truth and logic]
Bosk asked me to take a look at this (or suggested I might find it interesting).
Since there are a lot of new folks floating around DTF these days, I'll share my background. By coincidence, Bosk and I were admitted to the California State Bar on consecutive days in 2001. His bar number is just over 600 lower than mine. For the first 12 years of my career, I worked for a firm in West Los Angeles that is well known for representing clients in the entertainment field, including record companies and musicians. I represented Sony Music, Warner Music, UMG, the members of Third Eye Blind, and Rob Halford (among many others). I'm familiar with the ownership structure of Judas Priest (at least as of 10-12 years ago) and the origins of Third Eye Blind as a legal entity (and one of the first things I did as a new lawyer was to dig through some old dusty boxes from when the firm represented the Doors to find the original partnership agreement signed by all four members).
Everything Bosk said is accurate. In the case of Dream Theater (and a lot of other bands), there are two corporations. One handles the music side of things (it's the entity that contracts with record companies), and the other handles touring and merchandise. I can't remember the exact names, but I believe one is called Ytse Jams, Inc. and is mentioned in the liner notes of all the recent albums. Each of these corporations has a set of by-laws that outline how the corporations are governed and managed. In addition, there may be what's typically called a band agreement to which the individual band members would be parties. That agreement may outline things like songwriting credit, continuing entitlement to royalties if a member leaves, etc.
The term "full member" has no universal meaning. For example, at the time I represented Rob Halford, Scott Travis, despite having been in the band over 20 years at that point (longer than any other drummer in the band's history), and despite appearing to all the world as something more than a "hired gun," was "only" a contract employee of one of the JP entities (I've heard that may have changed since then.
I have no knowledge of the various agreements that cover the inner workings of Dream Theater. However, my educated guess is that, when MP left the band, the corporate entities and/or the other four members had to buy out his interest in the two corporations. The negotiations for this buy-out were occasionally mentioned in the media, and I would LOVE to know how things played out. Ultimately, my assumption is that MP received a chunk of cash (possibly along with payments over time) in exchange for his ownership interest in the legal entities. Whether MP retained his ownership and control over copyrights in DT musical compositions is hard to guess at, but there was a lot of discussion around whether the remaining band members may have agreed to refrain from playing certain songs without MP in the band. This would be similar to the well-publicized agreement between Queensryche and Geoff Tate regarding performances of Operation: Mindcrime.
Anyway, none of us know whether MM came on as an owner of the DT corporations. The public statements about MM being a "full member" have no relevance to that issue. If MM was/is an owner, then there have been or will be the same sort of negotiations that went on with MP (or maybe they streamlined the agreements to make it easier). If not, then it would simply be a matter of what his independent contractor ("employment") agreement says. And, as before, I would really LOVE to see the agreements.
And, last, with MP rejoining, will he regain his ownership in the DT corporations (essentially undoing the "divorce" of a decade-plus ago)? Again, we'll never know.
I'm kinda brain-fried and tired right now, so I hope that was somewhat coherent and not boring (even though it may not have shed much light on anything).