You'll get a striking albeit unfair picture of the relationship of two Virgos by imagining the movie The Remains of the day. The main characters, played by Anthony Hopkins and Emma Thompson, while neither a solar Virgo, still relate to each other like pure, archetypical Virgos would, had there been any. Personal and intimate relations, love and passion do not always come naturally for Virgos, who instinctively keep a detached, professional attitude in some situations where one would think it wiser not to. Yet I do believe in the possibility of a quite nice and healthy Virgo-Virgo relationship.
Perhaps it is the gentleness of many Virgos, the care and attentiveness. All Virgos tend to soften up when they feel comfortable. The unassuming, prudent Virgin becomes a humorous, pleasant and talkative companion. So I also think a Virgo-Virgo relationship can go rather cute, these nitpicking human beings still having so much in common, when not constantly picking on the partner. They probably realize it wouldn't be necessary. Then the quirk - this couple will be an extremist couple. Either the famously anally clean and orderly nazi-ish partners, or the total laissez-faire bohemian hippie couple. Paradox is common with Virgo.