In the living/dining area (of a home I just purchased in a new city/state where I don't yet know an electrician) there are 5 outlets with the lower-half switched. I was attempting to eliminate switching of the dining area receptacles, and in one box fed with two (2) 3-wire romex plus ground feeds I removed the red wire to the lower hot side of the receptacle with a broken tab between the upper and lower outlets. I jumpered the upper and lower outlets effectively making both hot, but now the switch does not control other half receptacles.
You need to join any red wires from the boxes you modified such that the removed red ties into the "other" removed red (or whatever color was used) so that the circuit is carried to the next location.
So if a red wired screw (or so be it, backstab) had another wire on it, or with it, they need to be capped together in the back of the box.
It's very common for receptacles to perform "double duty" as splices for wires going onward from the receptacle.
For instance, in many installations, the white wire from the supply cable will be attached to a silver screw, and the white wire for the onward cable will be attached to the other silver screw. The two screws are tied together because the "tab" between them is not broken off.
This would be the electrical equivalent of the other way of doing it, where you simply run a short pigtail wire from one silver screw... Then join it, supply and onward white wires with a wire nut. This method is required in some cases.
Normally, I would expect the pigtail method to be used with the red and black wires in a configuration like yours, since with the tab broken off, each side has only one screw. However, many receptacles have "both screws and backstab" connections. You're only supposed to use one or the other. But it's possible to use both the screw and the backstab to splice supply and ongoing. A backstab is a hole in which a wire can be jabbed, typically near the screw. It's not very reliable since the wire is making contact only at 1 or 2 points, as opposed to the broad surface of a screw and pad.
I suspect that is how it was done.
Anyway, the right answer is to convert all the relevant connections from "screw and backstab" method to "pigtail and wirenut" method, of course no need for the pigtail on sockets you do not intend to wire that hot to.
The pigtail method can also be used to solve the other problem of connecting two wires to 1 screw. Instead of a jumper (and being forced to use the backstab or overload the screw), you can simply have a pigtail for each brass screw, so you are joining 4 black wires at the wire nut - supply, onward, and 1 to each socket.
Or, you can replace the receptacle with a new one, whose tab is not broken off. Receptacles cost between 50 cents and $3.