The Astro-trio

In any natal chart, because Mercury and Venus are so close to the Sun, Mercury is always either in the same zodiac sign as the Sun, or no more than one sign away before or after (28 degrees). Venus can be in the same sign as the Sun or no more than 2 signs away (47 degrees). There could be rare instances where these rules appear not to apply, but they must be few and far between.

So....for example, in my own chart Sun is in Aquarius, Mercury is in Capricorn and Venus is in Sagittarius. In my husband's Sun is Aries, Mercury Pisces, Venus in Taurus. Some of my husband's immediate family have Sun, Mercury and Venus all in the same sign.

So what do I find so significant about this? I suppose it's that quite a large part of anyone's personality is defined by this mix of up to 3 consecutive zodiac signs.
One quarter of the zodiac. This must produce defineable groups. One could look on each group's similarities as the melody being played, whilst the Moon, Mars, Jupiter and Saturn play their own solo improvisations.
Uranus, Neptune and Pluto being the bass beat, the generational flavour. The melody, though, is most memorable for listeners and to the player, and therefore very important.

I am not sufficiently mathematically adept to be able to calculate how many variations (groups) of Sun/Mercury/Venus there can be. It would be interesting to study examples of each type, ignoring all other components of the charts.

Some astrologers find significance in what order the Sun, Mercury and Venus rise. I do not find their theories on this too persuasive, however - but it does relate back to my own thoughts in one way.

Would an Aquarius Sun with Mercury and Venus both in Aquarius be more Aquarian than me - yes, of course! Most cook-book interpretations of an Aquarian would be likely to apply to that person. Would an Aquarian with both Mercury and Venus in Capricorn be less adventurous, restless, or prone to travel than me? Probably. How about an Aquarian with Mercury and Venus in Pisces ? A different animal altogether - more overtly mystic and dreamy, less organised. There must be dozens of combinations of just these 3 components, with their related elements and modalities.

Complexity upon complexity - and that's a VERY basic beginning.