Initiator levels of a multiclass martial adept with levels in a Tome of Battle PrC

[Abithrios]

The consensus of the Internet is that levels in a prestige class that explicitly gives full advancement of initiator level gives full IL progression to every initiator class that character has. My DM is skeptical, arguing that I would have to choose each level which IL goes up by 1 and which goes up by 1/2 (similar to how PrCs that advance spell casting work). I have not found anything persuasive that supports either opinion.

To be more explicit: the character in question would have levels in multiple ToB base classes and at least one ToB prestige class that gives maneuvers.

Is there any RAW, official ruling, or strong argument one way or the other on whether PrCs that give maneuvers advance fully all ILs or just one at a time?

[sleepyphoenixx]

ToB p.39, under "Multiclass Characters"

Prestige classes work a little differently. In most cases, you
add the full prestige class level to your martial adept level to
determine your initiator level. See the prestige class descriptions
in Chapter 5 for details.

The PrC's that add to IL usually have a line like

You add
your full bloodclaw master levels to your initiator level to
determine your total initiator level and your highest-level
maneuvers known.

[Abithrios]

ToB p.39, under "Multiclass Characters"


The PrC's that add to IL usually have a line like

You add
your full bloodclaw master levels to your initiator level to
determine your total initiator level and your highest-level
maneuvers known.

This seems to assume my initiator level is a single number. If I have multiple ILs would all of them increase at the full progression or only one? More importantly, why?

[Crake]

Another question to ask would be each time you get an additional known/readied maneuver and stance, does it add one to each initiator class you have, or to just one? It seems like if the answer to that is just one, then the increased initiator level is likewise just to one class.