All the people whose charts I've read are one sun sign and their whole personality is, of course, influenced by all the other planets and their placements.
Exactly so. But there is a widespread belief in Modern Astrology that there is a sort of transition space where two adjacent signs merge and influence each other. In part this is a natural consequence of Kepler, who rejected signs and went for degrees. The Zodiac becomes little more than a sort of orbital motorway - the M25 of the Cosmos.
Pre-Kepler it was seen more as a series of discrete houses through which the Sun passed and it was either in one house or the other but never two at once. But the tradition still allowed for variation within a sign. Not just at the beginning or end, but all the way through. That came from sub-divisions of a sign (rooms in the house, to use that analogy). the best known today being decans, And that's the only one that gets any use at all in the Modern practice.
So, bearing in mind Ronia's point about the role of the other planets, let's just consider a few factors here.
Firstly, there is one thing that we need to be careful of at the start:
I'm a June 20th Gemini and it definitely seems like I have a lot of Cancer traits as well. Just not sure what kind of affect it has...
The first question I'd ask here is are you sure you're Sun is in Gemini. Just because the Sun Sign Column says June 21st for Cancer, doesn't always make it so. I did a run of 30 consecutive Cancer ingresses. The earliest one occurred at 16:45 GMT (Universal Time) on 20th June. If you had been born on that day, in the USA, you would have to be born before 12:45 EDT to be a Gemini. If you are on the West Coast you can push back that local time into mid morning.
Most of the ingresses were on 21st but even that doesn't force you to be a Gemini' if the ingress was in the early morning in London. You might already have checked that for your birth year but it's worth stating for other readers of this thread.
Now let's consider the subdivisions.
The last decan of Gemini is ruled by the Sun. That would decrease the overall Mercury influence.
The first in Cancer is ruled by Venus
There are other divisions, one of the oldest is the Bounds or Terms
The last of these in Gemini is ruled by Saturn
The first in Cancer is ruled by Mars
Their influences would also be felt, Mercury or Moon set the overall tone but the Bound ruler adds shading to the tone.
There are even more subdivisions, but most were not regularly used in the West, though some made their way into Indian Astrology.
What can be applied to your Sun's position can be applied to every other position in your chart, thus your Capricorn Ascendant, lies in the Bounds of Venus and the Decan of Mars, And you Libra Moon lies in the Bounds of Jupiter and the Decan of Mars.
All of those subtly change a natal reading,
