We test the coarse-grained time-marching model we developed for predicting the linear viscoelastic properties of branched polymers from the knowledge of their molecular structure on several new model architectures. Based on three viscoelastic parameters, i.e., the Rouse time of an entanglement segment, the plateau modulus and the entanglement molecular weight, this model uses the ingredients of the tube-based theories of McLeish and co-workers, and its implementation is based on a time-marching algorithm. With a new way to account for the motion of the molecular segments localized between two branching points and within the framework of dynamic tube dilation (using the extended criteria of Graessley), this conceptual approach was already successfully applied to linear, star, H and pom-pom polymers. In this work, we extend our work to tree-like polymers. Then, based on the predictions obtained for the linear data, we extended the model for predicting the non-linear rheology, following the approach proposed by McLeish and Larson, and Blackwell et al. We consider in particular the case of model symmetric Cayley tree polybutadienes and poly(methyl methacrylates) having 2, 3 or 4 generations with branches of varying degree of entanglements. In addition to systematic linear frequency sweep measurements, we performed uniaxial elongation measurements using the SER fixture. The samples tested exhibited significant strain hardening compared to the linear analogues at lower and intermediate Hencky strain rates. The extracted effective steady extensional viscosity scales with the elongational rate with a power exponent of about -0.5, in agreement with earlier findings with linear polystyrenes.