Let's invert a trope. C'mon, it's fun. In this case the idea of everyone in a rpg party having completely different characters. Now having different characters each bringing different strengths to a venture is a good thing. You have your fighter, cleric, wizard, and rogue etc. In fact different fighters in a party can be very different in terms of weapons, attributes etc. Ditto Traveller where no two lieutenants in the Navy or Army are anything alike.
In fact rpgs have gotten downright meticulous in ways to individualize your character. Of course this level of detail is not covered in rules-lite system which is sort of my blogging theme/niche/passion. Of course you can make up whatever details, tweaks or whatever you want about your character, that don't affect the game and again play of two similar characters might be completely different. But again, just for kicks, what if everyone in the group plays the 'same' character?
Option #1 The players' characters are all clones of the same individual. How identical they are is up to the tech and dramatic license taken. They might have the same attributes but be trained differently or raised and trained alike a la Star Wars' Storm Troopers. Assuming memory transfer and identical mind sets people's personalities will probably diverge after a while or characters could get different hooks (one gets married, one get addicted, one becomes a reverend ... it all averages out.)
Option #2 The characters are all incarnations of a single 'Prime' character but from different time lines. They made different decisions creating different timelines and altering their skills and even stats more and more over time. You'd have to have some idea where each person diverged from the 'original' timeline and history could get very complex.
Option #3 The players are all the same person but from alternate Earths. So one might be a wizard, another a cyber-hacker, another a psionic detective etc. They would have similar skills and sats with some differences for culture and tech levels etc.
Option #4 Mass production! The characters are all the same model of robot/android. This is similar to #1 except the characters can be completely identical to the point of swapping skills and information they develop.
Option #5 Supers! The characters are all the same super who can make copies of himself. The GM might want to include a few NPC copies as well. When the super recombines the players' role is that of voices in their head. The GM might even make the original an NPC and make the 'copies' make rolls to persuade them to take a certain action or take over completely. Triad in the Legion of Super Heroes had this power. She was three identical women who combined to a single form. Each separate self had a very different personality (shy, extroverted and neutral)though when combined they tended to 'average' out. Since everyone on her planet had the same ability but identical personalities she was regarded as a nut job on her home world.