If the request is to have a new database field or link created, this will probably not happen according to the Help pages. The intent is to keep as much of the information as possible in the biography (text area), not to mention all of the other changes that have to happen to support a new field or relationship link (see the link for information).
There is however guidance on how to handle Non-Traditional Families, and/or Unmarried Parents. A key factor to consider is that even if they may not have been recognized as legally married, they may be considered legal partners, which we would consider the same thing.
The best option, in my opinion, is that you should use the biography to explain non-traditional family structures and simply use links to any parents or children that don't neatly fit in the family tree.
In short, the the general consensus has been that if you feel your long-term relationship could be described as a marriage, (common-law, civil union, civil partnership, domestic partnership, de facto) you should probably be listed as spouses even if your relationship does not carry the legal rights and duties normally assigned to spouses wherever you live. The only place this will get tricky is where children is involved, since our ancestry and research is more focused on genetic (blood) connections.
