The verb inundate means to give too much work or so many things they cannot deal with.
Synonyms are deluge, engulf, flood, or overwhelm.
The word origins from Latin (1620s) inundatus, past participle of inundare meaning “to overflow, run over”.
She will inundate them with projects and paperwork.
The customers are eager to inundate the representatives with calls.
The flood was able to inundate the communities.