A strategy combining a ditopic hydrogen-bond donor with two different hydrogen-bond acceptor molecules is proposed for the assembly of simple trimeric building blocks used in the construction of ternary cocrystals. The crystallization of each of three different low symmetry carboxyphenols (3-hydroxybenzoic acid, 6-hydroxy-2-naphthoic acid, and ferulic acid) with acridine and 2-amino-4,6-dimethylpyrimidine yielded ternary cocrystals where the three components are joined by phenol-pyridine and carboxylic acidamidine synthons. The use of pK(a) values, beta values, and synthon histories in the selection of the acceptor compounds is discussed. Significant challenges to the growth of the desired ternary products from solution were presented by competing crystalline phases, including the individual components, a variety of binary phases, salts, and hydrates. Molecular electrostatic potentials were used to analyze the donating and accepting abilities of the competing synthons.