The answer is yes, it exist non. Non-synaptic plasticity exists as you can read in "Non-synaptic neuronal mechanisms of learning and memory in gastropod molluscs" by Benjamin et al. and "Compartmentalization of Non-Synaptic Plasticity in Neurons at the Subcellular Level" by Nikitin and Balaban.
But the effect of hormones such as cortisol may also have an effect.
Non-synaptic mechanismmechanisms of regulation, and plasticity hasplay a very important role in the brain and isits ability to learn in many aspectaspects and at different scalescales.
A single cell can suffer internal modification that will modify eletrophysiological properties.
variationsVariations of concentration of elements in the CSF also have an effect.
Glia also hasplays an important role...
So, the brain is a very complex system with a lot of interdependent mechanisms of adaptation, regulation and plasticity. Synapse is just one aspect of it.