This is something I kind of wondered about for awhile. When Serge and Lynx switch bodies in Fort Dragonia, there is, from a strictly plot-based standpoint, this notion of equivalence. Serge and Lynx had to switch bodies because Search had drowned in one world and Lynx had died in that Dead Sea incident in the other.
But what thematic purpose did it have? It wasn't just a single flash-in-the-pale event. You play as Lynx for something like a third of the game.
I did some research on the concept of ego death late last year, and I was recently thinking that ego death could provide and interesting framework for the body switch incident, and, possibly, the nature of Serge's character as a whole.
Ego death doesn't mean actual, physical death, but rather the loss of ones sense of self -- in a sense. I don't claim to understand it fully, and there are a lot of different viewpoints about it, but one general way of looking at it is, through meditation or psychoactive drugs or some sort of trauma, losing one's sense of self, sense of separateness from ones environment, and feelings of control over ones own actions and... let's say "fate," just for fun.
What do we specifically know from the game's script? After Serge becomes Lynx, he ends up in the Cleft of Dimension, and during his escape from there, Harle has a few conversations about who he's become.
Here, you're presented with a few dialogue options. In one set, Serge initially maintains that he's Serge, and not Lynx. Harle, however, insists that nobody would believe he's Serge, and that Serge doesn't even exist in the particular world he's in. Thus, he must not be Serge.
And then she questions him on what Serge even was. This is the salient part: "Maybe for you it is evident, but... I wonder if you ever really were Serge...? Furthermore... what waz zis Serge? A figure, a shape? A spirit? A soul? Where waz zis Serge?"
I interpret this as a discussion on the illusory nature of Serge's ego. One of the dialogue options that follows in this exchange allows Serge to accept that he is Lynx. This, to me, amounts to Serge experiencing ego death.
Of course, this is really just half of it. Serge, obviously, gets his body back, and the flipside of ego death is the reformation of one's sense of self after experiencing it. There's also a couple of other themes about death and rebirth that come up a lot in the game.
One thing I do want to note is that Kato seems to have a fondness for gnostic mythology, dreamtime mythology, and Zurvanism (in some nominal sense at least).
There does seem to be a degree of overlap between the ego death, psychonaut group and the gnostic group, particularly through the idea of using ego death a as a means of achieving gnosis, although I'm not finding much concrete information about that.