K-Anonymization is an important approach to protect data privacy in data publishing scenario. Existing approaches mainly consider data processing with single constraint. There exist multiple constraints cases in the real applications, which makes the K-anonymization more complex. Simply applying the approaches with single constraint to the problem of multiple constraints may cause high information loss and low efficiency. Based on the idea of Classfly, a family of multiple constraints supported K-anonymization approaches named Classfly⁺ are proposed according to the features of mutiple constraints. Three K-anonymization approaches are proposed, which are naive approach, complete IndepCSet, and partial IndepCSet Classfly⁺ approaches. Experimental results show that Classfly⁺ can decrease the information loss and improve efficiency of k-anonymization.