The ever increasing video demands from mobile users have posed great challenges to cellular networks. To address this issue, video caching in radio access networks (RANs) has been recognized as one of the enabling technologies in future 5G mobile networks, which brings contents near the end-users, reducing the transmission cost of duplicate contents, meanwhile increasing the Quality-of-Experience (QoE) of users. Inspired by the emerging software-defined networking technology, recent proposals have employed centralized collaborative caching among cells to further increase the caching capacity of the RAN. In this paper, we explore a new dimension in video caching in software-defined RANs to expand its capacity. We enable the controller with the capability to adaptively select the bitrates of videos received by users, in order to maximize the number and quality of video requests that can be served, meanwhile minimizing the transmission cost. To achieve this, we further incorporate Scalable Video Coding (SVC), which enables caching and serving sliced video layers that can serve different bitrates. We formulate the problem of joint video caching and scheduling as a reward maximization (cost minimization) problem. Based on the formulation, we further propose a 2-stage rounding-based algorithm to address the problem efficiently. Simulation results show that using SVC with collaborative caching greatly improves the cache capacity and the QoE of users.