Interesting insights itt.
The game itself says that if more than 3 people travel through a gate, you get time-space difficulties which lead you to 'the point of least temporal resistance' aka the end of time. At least they came up with a canon explanation, but I always knew this was a cover-up for technical limitations.
I assumed it had to do with balancing the combat system. Having double and triple techs across 4 characters would've been fun, but also overpowered. Also, if you go through the script, the lines are somewhat similar but fitted to each character, so with 4 characters you might get redundant dialogue.
I think the above reasons, combined with the palette limitations Mauron mentioned, explains why they kept the limit to 3 members. I'm sure the dream team could've worked around one of these issues, but all of them together (combat, dialogue, palettes) were decisive.
Btw, there's a brief scene when you have a party of 4. It's at the end of your first visit to the future, when you first travel to the end of time. They made it work by assigning Robo as a 'follower' to your party, kind of like the cat in the millennial fair.
