I have 8 network runs from wall jacks to a patch panel in the basement. I want to extend a couple of jacks so that I connect another jack that I’ve added to another room. I know it’s not ideal, but essentially the two jacks would connect into the same port on my main switch also in the basement. What is the best way to do this? I have a keystone punch down jack but think it’s probably not good to punch another cable in there. Should I use a wall plate with screw down connectors with two cables? Or a double wall plate with 2 punch down jacks and wa switch?
Ethernet jacks cannot be wired in series. All modern twisted-pair Ethernet is a point-to-point connection with exactly two ends to each cable; it's not a shared bus and cannot be split passively.
(This was maybe doable with half-duplex 10 Mbps a few decades back, but since you went for Cat6 then presumably you expect reliable 1 Gbps links. Although there is technically a specification for half-duplex 1000BASE-T, it is generally not used in practice anywhere, and as far as I know, many Ethernet NICs just outright won't support it.)