Imagine that you are observing an enzyme-catalyzed reaction in the lab. Every time you add more enzyme, the reaction rate increases proportionally until the reaction rate suddenly levels off. No other chemicals were added, and no modifications were made in the experimental setting. Why do you think the reaction rate stopped increasing?

All the substrates are bound to the enzyme, thats why the reaction rate stopped increasing.

Explanation:

Actually an enzyme works by binding a substrate molecule to its active site, producing a product, resulting in an increase in the rate of reaction.

Enzyme + substrate = Enzyme + product

Whenever enzymes are added, reaction rate increases as the substrates are being bound to the enzyme's active sites but then occurs a stage where further addition of enzyme cannot increase the reaction rate because all the substrates have bound to the enzyme and there are no substrates left. Hence the reaction rate stopped increasing.