There are at least two words that can follow ASSURGENT.
There are at least two words that can follow SIGNATURES.
Add a P or an R to SIGNATURES to get the next word.
There is at least one word that can follow STRANGURIES. Early clue: add an F to get the word.
What was the word that we could have gotten by adding a P to "signatures"? (I was desperate to have someone find it, because I knew we could go from whatever that word is to "pasteurising"!)
When I saw the p, I thought 'supergiants;' I doubted that this was a word and then went on trying to think that the r word could be.
Looks like you get them both, drom: I just looked in m-w, and "supergiants" is a word! I figured the word that added a "p" probably started with "super," but I didn't come up with "supergiants."