The pseudo 1st order reaction happens when one of the reactant is in large excess and its concentration doesnt change during the reaction .
Is there any other such situation when a certain higher order reaction turns out to become a pseudo first order kinetic reaction (except the situation where an N$^{th}$ order reaction has N-1 species in large excess) ?
The Michaelis-Menten equation for enzyme kinetics is an example.
$v=\frac{k_{cat}E_0S}{K_S+S}$ where $S$ is substrate concentration and $E$ in enzyme concentration.
At low $S$ ($S\ll K_S$), the reaction is 2nd order with $v=\frac{k_{cat}}{K_S}E_0S$, i.e. first order in both enzyme and in substrate. However at high $S$ ($S\gg K_S$), the reaction is first order only in enzyme with $v=k_{cat}E_0$, and is zero-order in substrate. The substrate concentration doesn't have to be in molar excess to other reactants.
In chemical engineering, nonlinear systems such as higher-order reactions occuring in a continuous process at steady-state are often modeled using linear (which you can think of as first-order reactions) systems as an approximation for developing process control techniques. A MATLAB documentation page has some good information.
As a last example, consider an unstable molecule $A$. It can decompose to $B$ by two entirely separate elementary mechanisms. The first is $\ce{A + A -> B + B}$. The second is $\ce{A -> B}$. At high concentrations of $A$, the second-order kinetics will dominate and the decomposition of $A$ will be second order. But lower the concentration enough, and the reaction will become first order in $A$ because the rate the bimolecular reaction will be dwarfed by the unimolecular route at low $A$.
