The concept of peer-assisted content delivery networks (CDNs) lets other nearby altruistic clients forward requested content files instead of the source servers, which works to localize overall traffic. Our prior work proposed a traffic engineering scheme to localize traffic in peer-assisted CDNs. To induce altruistic clients to download content files that are most likely to contribute to localizing network traffic, this scheme combines the content files and allows them to obtain the combined content file while keeping the price unchanged from the single-content price. Although we have discussed how much traffic only a set of combined content files can theoretically reduce, we can expect further traffic localization by distributing combined content files to multiple altruistic clients. This paper proposes a periodic combined-content distribution mechanism based on our scheme. This mechanism determines when combined content files should be provided by considering the network cache state. Computer simulations confirmed that our new mechanism could double performance.