Recent developments in real-time ultrafast measurement techniques have enabled us to prove experimentally that soliton molecules execute internal motions with some aspects similar to those of a matter molecule. Such an analogy between the dynamics of soliton molecules and the dynamics of matter molecules is based on the assumption that the dissipative solitons constituting a molecule are rigid entities sharing a common profile. Whereas this assumption drastically reduces the number of degrees of freedom, it does not hold true in general and we demonstrate that it overlooks some of the essential dynamical features of the soliton molecule. We present a theoretical study based on the principle that the different pulse constituents of a soliton molecule are deformable entities. Specifically, by using of a collective coordinate approach to investigate bi- and trisoliton molecules, we reveal features such as symmetric or asymmetric distortions of their profiles, and energy exchange processes between them. This implies, in subsequent experiments, the use of characterization techniques that can be used to retrieve a larger number of degrees of freedom. © 2019 American Physical Society.