Can I Bind Multiple EIPs to a Load Balancer?

No.

• If you want to use the load balancer on a public network, you can only bind one EIP to the load balancer to receive requests from the Internet.
• If you want to use the load balancer in a VPC, bind a private IP address. To route requests from a different VPC, you need to create a VPC peering connection between the VPC where the load balancer works and the other VPC. For details, see section "Creating a VPC Peering Connection with Another VPC in Your Account" in the Virtual Private Cloud User Guide.