You other option is to cut out the worst sections following the lines of the ceiling joists and install new sections of drywall. If it’s as bad as your describe, you may decide to replace the entire ceiling.

1) Turn off the power at circuit breaker serving the receptacle circuit.
2) Verify the receptacle is dead with the voltage tester.
3) Remove and unwire the receptacle. Set it on the counter out of the way.
4) Disconnect and separate the black (hot) and white (neutral) wires.
5) Leave the ground wires connected for safety’s sake.
6) You should now have two black and two white wires exposed and separated from the outlet box.
7) Turn on the power at the circuit breaker.
8 ) Very carefully verify which of the two black (hot) wires is energized with electricity with the voltage detector.
Best to keep one hand in your pocket while doing this.
Only one black wire should be energized. Remember which black wire is hot.
9) Check if either of the white (neutral) wires is energized with the voltage detector – neither should be live.
10) Turn off the electricity at the circuit breaker.
11) Label the one black wire that was energized with a small piece of masking tape marked “line side”.
12) Wire nut together the two black wires coming from the outlet box.
13) Wire nut together the two white wires coming from the outlet box.
14) Turn on the circuit breaker.
15) Check if the downstream outlets have power.
16) No power in the downstream outlets? You have a broken wire in one of leads coming from the outlet box. Is there a sharp kink that would indicate a break?
17) Got power in the downstream outlets? You probably had a bad wire nut connection in your pigtail. Perhaps something came loose when you folded the wires in the wall box?
18) Turn off the power at the circuit breaker.
19) Wire the receptacle in parallel with the pigtail in the usual way.
20) Leave the receptacle hanging out of the wall box.
21) Turn on the power.
22) Check the wires for voltage with the voltage detector. Are the downstream outlets energized? Good.
23) Turn off the power.
24) Carefully fold the wires into the outlet box and remount the receptacle.
25) Turn on the power and recheck the downstream receptacles for power.

Let me know what you find. If you’re still having trouble, pictures would be helpful.

The correct approach is to remove the single gang box and install a double gang box. If retrofitting, cut a larger hole in the drywall to fit an “old work” double gang box. Use a cover plate that’s half blank (solid face) with an outlet profile on the side.

Keep in mind that while there’s not a specific limit to the number of outlets on a branch circuit, the NEC says the total load should be no more than 80% of the circuit breaker rating. So you may want to total up the current loads in AMPs for the TV, lamps, computers, portable electric heater, etc. to see what will be expected for the total load. If greater than 80% of the circuit breaker rating, consider pulling a new branch circuit for the receptacles to a dedicated circuit breaker.