  Scalar-tensor theories have drawn the attention of cosmologist for the past
few years because they can provide mechanism to explain the observable
phenomena. Moreover, the results of scalar-tensor theories can be applied in
higher-order theories of gravity. In this work, we consider a Brans-Dicke
scalar field cosmological model that includes a second scalar field minimally
coupled to gravity. For the second scalar field we consider the two cases that
there exist and there is not any interaction with the Brans-Dicke scalar field.
For the two models of our consideration we prove the existence of scaling and
de Sitter solutions. Furthermore, we perform an Obsiannikov's classification
for the field equations, where we find all the point and contact
transformations which leave the gravitational Action Integral invariant.
Conservation laws are determined and we show how these can be applied to infer
about the integrability of the cosmological models and find new analytic
solutions.
