Hi,
It's possible to create different birthday mails. Like one day before and another one four days before the birthday.
Go to Acymailing->Configuration->Plugins and click on the birthday plugin. Next click on Configuration. Set the new valkues and click on save. The second one will be added.
Please remember to create your birthday newsletter first and do not send it.
If you would like to work with different dates, that's also possible. Just create custom fields for them and in the configuration of the birthday plugin do not only select Acymailing as the source, but also the field you would like to use. If you leave it empty Acymailing will use the default birthday field.