Extension to the Stable Marriage Problem ? This may sound more like a social sciences question more than a TCS one, but it is not. When reading "Randomized Algorithms" which describes the Stable Marriage Problem, one can read the following (p54)  

" It can be shown that for every choice of preference lists there exist at least one stable marriage. (Curiously enough, this is not the case in a homosexual monogamous society with even number of inhabitants)...."

Are there any very simple extensions of the Stable Marriage Problem that allows some type of steady state that includes a homosexual monogamous society, or a society in which a certain subset of the population follow a different set of rules than the larger set ?

In the affirmative, are there algorithms that perform such a matching ?
There is an open conjecture regarding 3 types of people. Suppose you have men women and dogs so that men have preference lists on women, women have preference lists on dogs, and dogs have preference lists on man. Is there always a stable marriage? 

(For other preference structures on 3-types society the answers are known to be negative).

Another comment is that stable marriage represent a non empty core and there is a well known condition by Scarf that implies the existence of nonempty core. It is known that Scarf conditions are satisfied for the original stable marriage problemand for the house allocation problem. (But failed for the men/women/dogs problem).

Some references: 


A reference to Scarf's paper: H.E. Scarf, The core of an $N$ person game, Econometrica 35 (1967) 50--69.
A paper showing various applications for Scarf's crucial lemma and quote quite a few others: (In particular, a fractional version of Gale-Shapley theorem for hypergraphs by Aharoni and Holzman is described): R. Aharoni, and T. Fleiner, On a lemma of Scarf, J. Combin. Theory Ser. B 87 (2003), 72--80. 
A solution of the men-women-dogs problem when there are at most 4 of each gender appears in a paper by Eriksson et al (Math Soc Sci 2006).