Neuter Reactants: What do they do? So imagine a hypothetical chemical equation

$$
A + B \rightarrow C + B
$$

It is obvious from the equation that $B$ is not consumed during the reaction. If $B$ actively take part in the reaction, if it participates in the transition state and isn't just sitting there in the environment, I classify $B$ as a Neuter Reactant.

Under these defitions I would like to know:

Is a Neuter Reactant always a Reaction Inhibitor or Catalyst? 

or are there instances of neuter reactants $B$ such that their reactions $A+B \rightarrow C+B$ have a similar rates to the straight reaction $A \rightarrow C$?
There are reactions similar to the one you show, which is straightforward catalysis, these are autocatalytic reactions such as $\ce{A + B\to 2B}$ or $\ce{A + 3B\to 3B}$ which lead to interesting non-linear behaviour. Of more importance is the Michaelis-Menten scheme  $\ce{E + S\leftrightharpoons ES \to P + E}$ where E is an enzyme , S a substrate, ES a complex of both, and P the product.