Actually I found a solution myself. It was sufficient to duplicate the constraint multiple times, each time with a different column:
CONSTRAINT `RegistrationsInvoices1`
FOREIGN KEY (`RegistrationID1`)
REFERENCES `EBS`.`Registrations` (`RegistrationID`),
CONSTRAINT `RegistrationsInvoices2`
FOREIGN KEY (`RegistrationID2`)
REFERENCES `EBS`.`Registrations` (`RegistrationID`),
CONSTRAINT `RegistrationsInvoices3`
FOREIGN KEY (`RegistrationID3`)
REFERENCES `EBS`.`Registrations` (`RegistrationID`),
CONSTRAINT `RegistrationsInvoices4`
FOREIGN KEY (`RegistrationID4`)
REFERENCES `EBS`.`Registrations` (`RegistrationID`),
CONSTRAINT `RegistrationsInvoices5`
FOREIGN KEY (`RegistrationID5`)
REFERENCES `EBS`.`Registrations` (`RegistrationID`)
The only error was then just on the syntax of multiple constrains simultaneously. Thanks to @progman to pointing me in the right direction