The identification of electrical, mechanical, and biological systems using data can benefit greatly from prior knowledge extracted from physical modeling. Parametric continuous-time identification methods can naturally incorporate this knowledge, which leads to interpretable and parsimonious models. However, some applications lead to model structures that lack parsimonious descriptions using unfactored transfer functions, which are commonly used in standard direct approaches for continuous-time system identification. In this paper we characterize this parsimony problem, and develop a block-coordinate descent algorithm that delivers parsimonious models by sequentially estimating an additive decomposition of the transfer function of interest. Numerical simulations show the efficacy of the proposed approach.