There are no dangers (as in death, and the side effects have been covered by the other answers) to taking the morning-after pill too often.
EXCEPT that it might not work and you end up getting pregnant. “The Morning After Pill” is not as effective as “regular contraception” e.g. ring, patch, pill, IUD, implant, shot.
Its efficacy depends on where a woman is in her cycle.
So it is NOT recommended to take too often, simply because we hope you would use a more efficacious form of birth control if you really want to avoid pregnancy.
Side effects of the morning after pill include: nausea, vomiting, menstrual irregularities, dizziness, diarrhea, and/or breast tenderness.
If you have had an allergic reaction to levonorgestrel or “the morning after pill” before, do NOT take it.