How to find common ground between any zodiac signs?

I've been wanting to share my opinion about this topic of compatibility between signs, because many people, when discussing compatibility focus only on the element and aspects that particular signs form on the zodiacal wheel.

It is well known signs in the same element (Earth, Water, Air and Fire) have similarities, but they do not have the same modality. For example, although both are Fire signs, a Fixed Leo may seem stubborn and closed- minded to Mutable Sagittarius who appreciates flexibility and adaptability of ideas. (if you don't know what modality is please read this post). On a first glance signs that share modality do not get along because they form a square to each other (a hard aspect which implies difficulty and friction), but that is not the case. Of course signs who are fixed (Leo, Aquarius, Taurus and Scorpio) share their stubbornness and desire of stability and permanence. Signs who are Mutable (Virgo, Sagittarius, Gemini and Pisces) share the capacity to adapt to situations and people very quickly. Signs who are Cardinal (Capricorn, Libra, Cancer and Aries) share the desire to initiate and make the first move.

Another matter of compatibility is how the rulers of the signs get along. Aries and Sagittarius are both Fire signs and are considered compatible through the element perspective, but, one is ruled by Mars and one by Jupiter. These planets do not get along. Mars is a malefic planet focused on immediate action and self-gratification, while Jupiter is known as the Great Benefic and is associated with wisdom, morality and the higher mind. Sagittarius and Virgo are considered incompatible by element. Virgo is an Earth sign and Sagittarius is a fire sign. Now lets look at their rulers: Mercury and Jupiter. Both are intellectual planets, and in its pursuits for information Virgo is similar to the higher knowledge seeking Sagittarius. Another example is when apparently incompatible signs share the same ruler. Taurus and Libra may seem like they have nothing in common because Taurus is a Fixed Earth sign and Libra is a Cardinal Air sign. On the zodiacal wheel they form an inconjunct (an aspect which shows that the signs in aspect have nothing in common), but they are both ruled by the planet Venus, and in this where they find common ground.

Of course there is a lot to compatibility besides Sun signs, but I wanted to point out that even this topic is extremely complex.