The range of combined matrices and doubly quasi-stochastic matrices of order 3

Since a characterization of the 3 by 3 real matrices whose combined matrix equals a given doubly stochastic matrix has recently been obtained (by a group that includes some of the present authors), it is natural to turn to the related problem of determining the conditions that the entries of a given doubly quasi-stochastic 3 by 3 matrix must satisfy in order for a real matrix to exist whose combined matrix is precisely that doubly quasi-stochastic matrix.