Yes you can do this if you wanted to add a 2nd wired AP to the network system.
Any of the DAP series home models would work. Since this is a 2.4ghz only router, you could add a 2.4Ghz only AP like the DAP-1320, or 1360. Now you can install a DAP-1522, 1525 or 1533 which have both 2.4Ghz and 5Ghz radios. If you wanted to do some future proofing, you could add the DAP-1650 which has 2.4 and 5Ghz support along with AC modes too. This would be a great WiFi upgrade.
Only thing you need to make sure is that if you install a 2ndary WiFi AP that using 2.4Ghz, you can use the same SSID and PW as on the 645, just make sure that the channel being used on the AP is different. I recommend putting the 645 on manual channel 11 and the AP on channel 1.
You'll be good to go.
Some additonal info:
Bridge Mode vs Relay vs Acess Point (AP) / Routers vs Dedicated Access Points (AP)Turning a router into an AP.Let us know what you go with.
I have a DIR-645 and need to extend it through several walls to the back of my house. Can I run an ethernet cable from the DIR-645 and connect it to some kind of access point in the back of the house, which would then let me use my computer in the back of the house to create a wireless connection to the new access point? If so, what DLink access point models will work in this configuration?