Changing the order of the reaction with change in concentration
You would change the reaction speed, but not the order.

The order of the reaction can be changed by reagent concentration, if it is result of multiple reaction steps with different orders. By variation of concentrations you can manipulate the relative reaction speed,
as the order is often ruled by the slowest reaction.

Let suppose the 2 step reaction 
$$\begin{align}
\ce{2A + B &amp;-&gt; C} \\
\ce{A + A &amp;-&gt;[slow] D} \\
\ce{B + D &amp;-&gt;[fast] C} \\
\end{align}$$

For small $c_A$, the reaction speed
$$\frac{dc_C}{dt}=k_{low A}.{c_A}^2$$.

For high $c_A$, the first reaction becomes faster then the second.

$$\frac{dc_C}{dt}=k_{high A}.{c_A}^2.c_B$$.

You can also change the effective order of reaction, if some reactant is in about constant abundance and is not explicitly considered.

E.g. The speed of the reversed esterification
$$\ce{R1COOR2 + H2O -&gt; R1COOH + R2OH}$$ is the reaction kinetics of the 2nd order. But in abundance of water, it is effectively a reaction of the 1st order:
$$\frac{dc_{\ce{R1COOR2}}}{dt}=-k_1.c_{\ce{R1COOR2}}$$.