We introduce an imitation learning-based physical human-robot interaction algorithm capable of predicting appropriate robot responses in complex interactions involving a superposition of multiple interactions. Our proposed algorithm, Blending Bayesian Interaction Primitives (B-BIP) allows us to achieve responsive interactions in complex hugging scenarios, capable of reciprocating and adapting to a hugs motion and timing. We show that this algorithm is a generalization of prior work, for which the original formulation reduces to the particular case of a single interaction, and evaluate our method through both an extensive user study and empirical experiments. Our algorithm yields significantly better quantitative prediction error and more-favorable participant responses with respect to accuracy, responsiveness, and timing, when compared to existing state-of-the-art methods.