I have a standard 15A duplex outlet that is middle-of-run and backwired in my family room. I want to tap into this outlet to install a brand new outlet in a closet on the other side of the wall.

I'm pretty handy with basic home electrical work, but want to verify something - can I just tap into the family room outlet using the screw terminals (as noted above, both sets of backwire slots are in use).

That would be a simple way to get the new closet outlet installed, but not sure if having three connections on one outlet (i.e., two existing backwire sets and adding one set of screw terminals) is "in code" or something potentially dangerous? FYI - the existing family room box is deep, so no wire capacity problems...I just want to avoid having to create a "pigtail" and tap the new outlet directly into the screw terminals of the existing family room outlet.

The new closet outlet will have low draw - just some recharging units for small vac, etc.

Thanks!