  We extend inner fluctuations to spectral triples that do not fulfill the
first-order condition. This involves the addition of a quadratic term to the
usual linear terms. We find a semi-group of inner fluctuations, which only
depends on the involutive algebra A and which extends the unitary group of A.
This has a key application in noncommutative spectral models beyond the
Standard Model, of which we consider here a toy model.
