This is a job I did in a 1930s Cleveland Heights home. The coved breakfast nook ceiling had portions of the original "drip" texture around the perimeter but the field had been repaired multiple times from water damage with mismatched textures.
First, whenever demolition is involved, I cover the floors and nearby windows with heavy protection.
Second I quarantine the work area with plastic.
Fourth, I apply a bonding agent and repair the plaster.
And last I apply the original "drip" texture to the entire ceiling.