In a previous article [JDSGT17, 267-295, 2019] we have extended to countable shifts the notion of multifractal pressure previously introduced by Olsen [J. d′ Analyse Math131, 207–253, 2017]. This kind of pressure is defined by considering in the ”partition function” only those configurations which are ”multifractally relevant”. In this article we continue working in this direction and consider a pressure of this nature, but for suspension flows over countable shifts.