Outlet wire question (DIY)

Hello

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I am replacing some of the old outlets at my home and most of the old outlets are backstabbed so I end up just cutting the wire off of the old outlet and I am reconnecting the wire to the new receptacles using the side screw terminals, Most of the outlets have the usual 2 black, 2 white, and a ground wire.

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My question is can I take the 2 black wires and cut a 3rd separate piece of wire and then pigtail* the 3 together and then I would just have to connect 1 black wire to the receptacle? (I would want to do this with the white wires as well) The reason I am asking about this is because since the receptacles were mostly backstabbed they typically don't have enough wire to attach to the screw terminals (well they probably could but it wouldn't really come out of the wall box if I did that) so I end up having to extend each wire.

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*Just incase I used the wrong term, I am wanting to connect 3 wires with a wire nut or a push connector.

Edit: I'm in the USA, I assume code varies from country to country.