Adding asteroids and other “non-standard points” to the composite chart brings more detail to composite chart analysis.
Look to Eros for mutual passions, erotic connections, and obsessions in the relationship, for example. Look to Psyche for intuitive connections. Look to Juno for “me-you” relationship power dynamics. Look to Ceres for nurturing connections. Look to Vesta for dedication and commitment.
Asteroids can be read much like other planets — in terms of aspects they make to each other, as well as their placement by house. You need to know the basic meaning of each asteroid in order to understand how they function.
For example, a troublesome Eros in the composite chart could be indicative of the need for seemingly constant attention and feedback from one another. The erotic, lusty connection between you can produce conflicts. A strong, mostly positive Vesta can indicate a strong feeling of dedication and commitment to one another. A strong, challenged Vesta might suggest conflicts arising from your dedication to one another or to the relationship itself.