Although connected vehicle (CV)-based signal coordination has some proposed prototypes and has been investigated by several different strategies, the existing works have issues that require attention, including additional CV-based system uncertainties and platoon priority request considerations. Thus, a generalized framework consisting of a platoon-based bicyclic coordination diagram (Bi-PCD), a new probabilistic surrogate quantification, and a platoon priority-based offset optimization in the CV environment is proposed to improve the coordination performance. The proposed Bi-PCD extends the scope of the current Purdue coordination diagram (PCD) and its variants by covering extra practical and emerged variables. A prototype and field tests in a CV test pilot for general scenarios were implemented in a typical arterial road to verify performances of the proposed Bi-PCD and the offset optimization method. Field results demonstrated that using Bi-PCD could obtain explicit platoon features in both limited and full CV penetration conditions. The comprehensive analysis showed that the proposed Bi-PCD and the platoon priority-based offset optimization could further improve performances of the signal coordination.