Preposition after 'deluged'
We use by, not with, to talk about the action of something:
He got into the house by breaking the window. (action)
Not: … with breaking the window.
We use with, not by, to refer to the object or instrument that we use to do something!
He broke the window with a rock. (object/instrument)
By: Cambridge Dictionary - https://dictionary.cambridge.org/us/grammar/british-grammar/by
Essentially, with by, there is a matter of being once removed from the event itself, whereas with with, it is directly embroiled in the event. In a comment, I suggested "deluged by a rogue wave". The wave no longer exists, it being destroyed in the event, so by seems more apt to me.
I would use with in "deluged [with/by] phone calls" if the issue was mostly about the inability to handle the incoming calls. But I can see "deluged by phone calls" if the focus is on the people who are calling or the issue that precipitated the calls - as in "their announcement outraged the public, and for days they were deluged by phone calls and mail." After all, there are two ends to a phone call, and you can choose the preposition which best suits the end receiving focus.
I'll take a stab at it (without going through all the comments).
It really depends on agency (i.e. blame -- who's fault it is). Consider:
- Deluged by puppies
or:
- Deluged with puppies
Now. Everyone loves puppies, so you can hardly blame them for your distress. Someone must have left them on your doorstep, or sent them through the post, or maybe you just allowed your dog to get pregnant (again). But it's not the puppies fault. You have been deluged with puppies, not by puppies.
On the other hand:
- Deluged by spammers
or:
- Deluged with spammers
You have my sympathy if you find yourself unable a cope due to a surfeit of spammers. However, it is unlikely that some mean soul sent them through the post, just to annoy you. Spammers have agency. They could have decided to stay in bed, or get a proper job, or something. You have been deluged by spammers, not deluged with spammers.
OK. Now you can jump on me. [Waits for the deluge]