What is a birthday? It commemorates years of existence.
But what other chronological milestones?
A kiloday is 1 000 days.
(A hectoday is 100.)
So in addition to your yearly birthdays, you can have a kiloday celebration every few years.
For example, in your 28th year (when you are
27), you'll be 10 000 days old!! This calls for a celebration.
Similar is true when you are 54 and about 82.
Now if you are a big fan of these celebrations, you might go for the Hectoday celebration. You'll get 2 or 3 of those a year.
Then there are Moon celebrations. Around your 17th year (when you are 16), you'll be 200 moons old.
We can also use solar rotations and orbit of other planets. At 24 you can celebrate your 2nd Jovian Birthday (and before friends plant your face into a cake).
This is great if you wish to ingratiate yourself with someone, yet their birthday is months ahead/behind.