Concentration of excess reactant If increasing/decreasing the concentration of an excess reactant influenced the percentage yield of a product experimentally, how could this be explained?

I know that in theory, the excess shouldn't affect the yield- since it's the limiting that decides how much is produced. But is there any possible explanation for this result?
A very typical situation in organic chemistry is the following:

$\ce{A -&gt; undisired products}$
$\ce{A + B -&gt; target product}$

Here it is easy to see that increasing the concentration of $\ce{B}$, we will get a higher yield of the target product.
The other reaction can be of many kinds.
$\ce{A}$ can decompose in the reaction medium, can react with itself, with the solvent, with byproducts form the desired reaction, etc.