  A semilinear version of parabolic-elliptic Keller-Segel system with the
\emph{critical} nonlocal diffusion is considered in one space dimension. We
show boundedness of weak solutions under very general conditions on our
semilinearity. It can degenerate, but has to provide a stronger dissipation for
large values of a solution than in the critical linear case or we need to
assume certain (explicit) data smallness. Moreover, when one considers a
logistic term with a parameter $r$, we obtain our results even for diffusions
slightly weaker than the critical linear one and for arbitrarily large initial
datum, provided $r >1$. For a mild logistic dampening, we can improve the
smallness condition on the initial datum up to $\sim \frac{1}{1-r}$.
