Amsterdam-Taipei-Beijing-Amsterdam

Hello! We booked a multi destination flight from Amsterdam to Taipei and return from Beijing to Amsterdam with KLM. We still need to book our flight (other company) from Taïwan to Beijing. We have doubts if we are eligible for the 144h transit because it's not a stopover but a flight we are going to book separately to be able to stay 6 days in China. Do you think we are eligible? Thank you very much!