We examine a one-parameter class of actions describing the gravitational interaction between a pair of scalar fields and Einsteinian gravitation. When the parameter is positive the theory corresponds to an axi-dilatonic sector of low-energy string theory. We exploit an SL(2,R) symmetry of the theory to construct a family of electromagnetically neutral solutions with non-zero axion and dilaton charge from solutions of the Brans--Dicke theory. We also comment on solutions to the theory with negative coupling parameter.