My first question (that I suspect nobody can answer) is whether we can trust these three birth times of 3:57, 3:58, and 3:59. I imagine they're close, and I'm sure the birth order is correct - that is probably the most important legal consideration the medical staff needed to get right.
Births
can appear this fast, but usually are separated by several minutes. Knowing triplets were due, the hospital in 2000 would have had special staff on hand for the event if it was planned, so I wouldn't be surprised if they were highly efficient, but this is still unusually fast for three deliveries.
Besides, it was within a few minutes while Neptune was exactly angular. People make stupid mistakes
Nonetheless, let's assume the three are correct and go forward with the exercise you propose.
First, psychological studies of twins (which likely apply to multiple births) show that they are far more alike than is always visible but there is variability - from one set of twins to the other - with how much they
like to seem alike. I have found this varies with the relative strength of Venus vs. Mars. Twins with very close Venus angularities or other defining marks take great pleasure in seeming the most mirror-like of each other. Those with Mars dominant (planet of sibling rivalry) have the greatest pleasure from greater ego-distinction. In this case, we have a Taurus Sun partile conjunct Venus but 5° from conjunct Mars. I read this as: They have lived their lives mostly being (and loving being) "the same," but with a secondary streak of each trying to find his particular quirks or distinctions to stand apart.
They all have Neptune on the angle. It gets closer with each birth, the first one having Neptune 1°23' from IC and the last one (the only one partile) has it 0°52' away. There isn't really much difference here but, in their course of ego-distinction, the youngest would likely single himself out as the more Neptunian.
None of them have major fixed stars within 1° of an angle. There are no Moon or other aspects that make a difference. Were we to consider houses, there are no house shifts or significant changes in relationship to the cusps. Minor factors like Asc and MC signs remain the same.
We can spend some time on the midpoints that involve angles. This might be our most fruitful avenue. Sticking only with 90° modulus within 1° (there is a limit to how much time we can spend on this, but you might want to dig further on this perspective if interested), we get the following (I will underline those that are unique to one of them and not the others)
Triplet 1 has
MC=Me/Ur (54'), Ur=Pl/As (21'), Ju=Su/As (5') =Ve/As (33'),
Su=Ur/As (60'), Ve=Ur/As (4'),
Ma=Sa/MC (58'), Me=Ma/MC (23')
Triplet 2 has Ur=Pl/As (15'), Ju=Su/As (11') =Ve/As (38'), Ve=Ur/As (10'), Me=Ma/As (16')
Triplet 3 has Ur=Pl/As (10'), Ju=Su/As (17') =Ve/As (44'), Ve=Ur/As (16'), Me=Ma/MC (8')
Looking at more obscure astrological factors that may (or may not) have significant astrological value, we find all three have the asteroid Vesta square Ascendant, getting closer with each successive birth.
I have one more item of possible great significance to check.