An individual experiences double coverage when he benefits from more than one health insurance plan at the same time. This paper examines the impact of such supplementary insurance on the utilisation of health care. Its novelty is that within the context of count data modelling and without imposing restrictive parametric assumptions, the analysis is carried out for different points of the conditional distribution, not only for its mean location.We use data for Portugal on the consumption of doctor visits, taking advantage of particular features of the public and private protection schemes on top of the statutory National Health Service. Results indicate that double coverage generates additional utilisation of health care and, even though it is present in the whole outcome distribution, by looking at different points we unveil that the effects are relatively smaller for more frequent users. Another interesting finding regards the source of supplementary insurance since although both public and private second layers of health care protection increase the utilisation of doctor visits, it adds more to the consumption when provided by private organizations.