Yes. It's very common for an organization to run multiple birthday eCard campaigns at the same time. For example, you can have a birthday eCard campaign for employees, one for customers and another one for volunteers.
You might also need to subdivide those birthday eCard campaigns into even smaller groups of contacts. For example, you might have a birthday eCard campaign for customers who subscribe to your email list and another for your VIP customers who get a different, more substantial discount for their birthday.
You can have an unlimited number of email lists and an unlimited number of automated email campaigns. Everything is included with no 'surprise' fees.