Keep in mind that a trained voice should not actually have a passaggio at all! Your vocal apparatus consists of muscles (vocals muscles) and ligaments (vocal cords). Pitch is determined by the tension as well as the weight. This is the reason why our voice get lower if we are sick (as inflammations cause blood to be pumped into the vocal muscles and thus increase the weight).
Now we can control the vocal muscles to have it soft enough to vibrate fully, partially or to only have the vocal cords vibrate. The more vocal muscle vibration we add the stronger heavier and lower our voice gets, the less we add the lighter, more flexible and higher our voice gets.
The concepts of vocal registers is nothing but a few extremes in this: Chest voice is what happens when you have a lot of vocal muscle vibrating, head voice is when you have little to no vocal muscle vibrating. Then you have the voix mixte which is when you have have some amount of vocal muscle vibration.
As I said already pitch depends on weight, so there is a limit on how high or low you can get in some register, which means you need to change into a different register, which is the passaggio. Now as these are just arbitrary points in vocal configuration there can be more registers and thus more passaggios, but traditionally we consider a lower and an upper passaggio.
But this is not a necessity, but a habit. If we can develop control over our vocal muscles we can steplessly add and take mass as we go along. So instead of taking one vocal control to its limits and then having to change we can change the configuration continuously on the way there, eliminating the very concept of registers (not exactly, because we still get registers formed by different techiques, but this is not relevant for the concept of passagio) and instead forming a single, big register that can effortlessly go from the lowest to the highest notes.