Why doesnt the overall rate of a reaction increase if you increase the concentration of a reactant in a non rate determining step?
Let's think about this reaction:

$\ce{ A + B-&gt;[k_1][] C + D -&gt;[k_2][] E }$

let's say $k_1 &lt;&lt; k_2$ so the first reaction is much, much slower than the second step (at equal concentrations) 

Now it get's a little bit tricky since the reaction rates depend on the concentration. Let's assume for now that the concentrations of $A$, $B$ and $D$ are in a way that the reaction rate of the first step is really much faster than the second step.

What happens is that $A$ and $B$ react to $C$ quite slowly, but once you got any $C$ it reacts very fast with $D$ to $E$. This means your concentration of $C$ will always be quite low, since everything that is produced will react to $E$. But this also means that the concentration of $E$ is basically increasing with the rate of the first step. The slow reaction part is limiting the overall rate.

What happens if we increase the concentration of $D$? Well, the second step will be even faster, so all the $C$ that comes out of the first step will be converted to $E$ even faster. But the first step is still slow, so your $E$ concentration will still increse approximately with the rate of the first step.

Only if we would reduce the concentration of $D$ to very low levels (much lower than $A$ and $B$) we would see a difference, in that case the second reaction will get slower than the first one (reaction rate depends on concentration) and will be the limiting step.