Towards parton distributions with fitted charm

Modern parton distribution function fits require an accurate treatment of heavy quark mass effects. In this contribution, we discuss how the FONLL general-mass variable flavour number scheme can be extended to allow for the possibility of a fitted charm PDF. We present a first estimate of the impact of a fitted charm contribution in the FONLL structure functions, and we discuss the development towards including a fitted charm PDF in the NNPDF framework.