Internetware has been an emerging software paradigm to best support computing in the Internet era. Internetware emphasises accommodating the open, dynamic and uncontrollable natures of Internet, which directly and indirectly relates software evolvability. This paper observes that evolving non-Internetware software into the Internetware paradigm and evolving software within Internetware will be two main research and practical issues, and hence proposes an integrated approach to address these two issues. The proposed framework is based a three-dimension structure, with System Functions, System Quality and System models as dimensions. With this framework, evolving software into internetware paradigm can be viewed mainly as changing the qualities of existing software and evolving software within Internetware paradigm can be viewed mainly as changing software functions. The involved prototype tool, working examples and experiments conducted, are used to illustrate the proposed approach.