New to BIG IP and have a requirement to load balance between two pools

Can BIG-IP Version 4.5 pool have VIPS as members and load balance between two pools? The VIPS which are members will map to two different pools with real servers. The requirements that I have are one public IP mapped to the internal VIP IP. This internal VIP IP is called MAIN_VIP attached to MAIN_POOL. The MAIN_POOL has two members called VIP_A and VIP_B. VIP_A is attached to POOL_A, and VIP_B is attached to POOL_B. Those pools have real servers that will process the request of MAIN_VIP. Thanks for everyone who read this. Regards, JR