We investigate two-field theories on a j-surface and a conical stalk. First we study two-field theories on a j-surface with a conical stalk. Then we study two-field theories on a j-surface with a conical stalk and a toric conical stalk. Finally we study two-field theories on a j-surface with a conical stalk and a toric conical stalk. We compute the effective coupling between the two-fields.