Surányi (2006) observed that Hungarian has a hybrid (strict + non-strict) negative concord system. This paper proposes a unified analysis of that system within the general framework of Zeijlstra (2004, 2008) and, especially, Chierchia (2013), with the following new ingredients. Sentential negation nem is the same full negation in the presence of both strict and non-strict concord items. Preverbal senki ‘n-one’ type negative concord items occupy the specifier position of either nem ‘not’ or sem ‘nor’. The latter, sem, spells out is ‘too, even’ in the immediate scope of negation; is/sem are focus-associating heads on the clausal spine. Sem can be seen as an overt counterpart of the phonetically null head that Chierchia dubs NEG; it is capable of invoking an abstract (disembodied) negation at the edge of its projection.