I would leave the current can in place as a wiring enclosure where you can make all the splices and have them protected, as well as providing easy access should there ever be problems.
You have a couple of choices for making the splices between the old cables and the extensions.
You can use B-connectors to make crimped splices between the old and the new. The problem is keeping them all neat. For just a few cables, this will be fine.
Or, you could mount some 66 or 110 punch down blocks in the can and make the connections through the blocks.
For wires heavier than 22 gauge, you won't be able to use the punch down blocks. You could use B-connectors or screw type terminal strips for these.
Be sure to label all the cables on both sides so you know what they all go to.