In this paper, the indirect signal production system with nonlinear transmission is considered ut=Δu−∇⋅(u∇v),vt=Δv−v+w,wt=Δw−w+f(u)in a bounded smooth domain Ω⊂Rn associated with homogenous Neumann boundary conditions, where f∈C1([0,∞)) satisfies 0≤f(s)≤sα with α>0. It is known that the system possesses a global bounded solution if 0<α<4n when n≥4. However, in the case n≤3 and if we consider superlinear transmission, no regularity of w or v can be derived directly. In the current work, we show that if 0<α<min{4n,1+2n}, the solution is global and bounded via an approach based on the maximal Sobolev regularity.