I mistyped Bianca. She is a healthy Four, which operates like a One. The critical and analytical Virgo that she is threw me off too.
The emphases below are mine. Take all this with a grain of salt -- Personality types in my experience expose only a fraction of who the individual really is.

Enneagram Type Four (the Individualist)
with
Enneagram Type Four (the Individualist)

What Each Type Brings to the Relationship
As with all double-type relationships, two Fours generally bring the same qualities to each other. Thus, the Level of health of each person is especially important for these types of relationships as are their dominant instincts. Double Four pairs generally make good friends and deep friendship is something they often bring to their intimate relationships. Fours often feel misunderstood, yet feel a special bond of understanding with other Fours. They share stories of their childhood traumas, their private dreams and disappointments. Both types are openly emotional and sensitive to the needs of the other. Both are looking for adequate mirroring and in a double Four relationship, they have a real possibility of finding it.

Because each person in a double Four couple is so attuned to their own emotions, there is a great deal of sensitivity and respect for individuality and each other's emotional needs. They have the ability to laugh at themselves and to find amusement with each other in the dark loneliness of the childhood and adolescence. They are not put off by unearthing deep psychological and personal issues. Both are encouraging of the artistic and creative efforts of the other and find it easy to communicate about the most private and intimate issues as they arise. They feel that their relationship is a truly safe space where the other is on a similar emotional wavelength: both feel less alone and less like something is wrong with them personally. Double Fours are highly romantic and idealistic as a couple and their intimacy has the potential to grow into a grand passion of virtually operatic proportions. Emotional ups and downs, hopes and disappointments, elation and despair tend to make this couple more focused on itself than on practical life, child raising, or their careers. Enormous candor, deep friendship, and consideration for the unique history and emotional needs of the other would be hallmarks of this relationship.

Potential Trouble Spots or Issues
Emotional instability of the relationship itself is the main potential problem with a double Four intimate couple. Each person can be self-absorbed and excruciatingly aware of what he or she is getting (and not getting) in the relationship. Both want to be the focus of attention regarding emotional issues. Both want special handling—and insist on having special needs and they can resent the other for demanding the same for themselves. Both long for an ideal mate—and the feeling that one has found it—can alternate with depression (and other reactions) when expectations are disappointed. They can get into "Who's more damaged?" contests, a form of negative competition. Both are more or less secretly looking for a rescuer and can get lost in a morass of emotional drama even if they find one.
For all of their potential sensitivity, Fours also tend to withdraw from others and to withhold their attention and affection when they are having a conflict with someone. Fours have a profound lack of trust in others, and this lack of trust can extend even to their intimate partner. A period of testing will invariably happen that may be too much for the other Four to bear. They can be annoyed by the other's quirks and "sensitivities" and unacknowledged demands. They can be intolerant of the other, making each other walk on eggshells, ironically making it difficult to bring up certain issues with the other.

Double Fours can become moody and incommunicative, passive-aggressive, and disdainful, actually hating the very person they may have been so passionately in love with. Rejecting the other (and feeling rejected) can alternate from both parties. Arguments can spiral out of control and hurtful things get said until reconciliation becomes difficult, if not impossible. Once certain things are said in the heat of the moment, they can never be taken back. Permanent damage is done to feelings of trust and safety—and to the future of the relationship. Once hope for the relationship dies, it is difficult to resuscitate.