What happens if too much phenolphthalein is added to an acid?

Phenolphthalein is weak organic acid. It is used as an indicator in acid base titrations. We usually use a few drops of the indicator to see the color change at the end point of the titration. Say we have an acid HCl being titrated with a base NaOH. If we add too much phenolphthalein, it would alter the concentration of the acid HCl being titrated. So, the volume of NaOH required for the titration would be slightly higher than it would be if phenolphthalein was not present in excess amounts. So the addition of too much phenolphthalein leads to the overestimation of the concentration of the acid being titrated.