In real chemical reactors, it is mostly inevitable that multiple reactions will occur. One of the common types for this is parallel reactions where the reactant can react in two reactions to form two products.
Consider the general reversible parallel reactions $$A\xrightleftharpoons[k_{-1}]{k_1} R$$ $$A\xrightleftharpoons[k_{-2}]{k_2} S$$
Assuming that the reactions are first order we get three coupled rate equations,
$$-\frac{\text{d}C_A}{\text{d}t}=k_1C_A-k_{-1}C_R+k_2C_A-k_{-2}C_S$$
$$\frac{\text{d}C_R}{\text{d}t}=k_1C_A-k_{-1}C_R$$
$$\frac{\text{d}C_S}{\text{d}t}=k_2C_A-k_{-2}C_S$$
These three coupled differential equations can be solved numerically (though there are analytical solutions for some simplified cases, e.g. no reversible reactions).
The graph below shows the change in the concentration with time for the components for relative reaction rates, with initial concentration of $C_A=1$. If $k_{-1}=0$ and $k_{-2}=0$ then the reactions are not reversible.
Explore how the variations in the relative reaction rates affect the concentration of the components with time.