Proxy Re-Encryption (PRE) is a favorable primitive to realize a cryptographic cloud with secure and exible data sharing mechanism. A number of PRE schemes with versatile capabilities have been proposed for different applications. The secure data sharing can be internally achieved in each PRE scheme. But no previous work can guarantee the secure data sharing among different PRE schemes in a general manner. Moreover, it is challenging to solve this problem due to huge differences among the existing PRE schemes in their algebraic systems and public-key types. To solve this problem more generally, this paper uniforms the definitions of the existing PRE and Public Key Encryption (PKE) schemes, and further uniforms their security definitions. Then taking any uniformly defined PRE scheme and any uniformly defined PKE scheme as two building blocks, this paper constructs a Generally Hybrid Proxy Re-Encryption (GHPRE) scheme with the idea of temporary public and private keys to achieve secure data sharing between these two underlying schemes. Since PKE is a more general definition than PRE, the proposed GHPRE scheme also is workable between any two PRE schemes. Moreover, the proposed GHPRE scheme can be transparently deployed even if the underlying PRE schemes are implementing.