Both Uses

vengeance
in
Misery, by Stephen King
(Auto-generated)

He might have believed that the fever Dr. Shinebone had almost gleefully predicted had come on him at last, and with a vengeance, but it wasn't fever which had simultaneously brought wild red roses to his cheeks and tugged his forehead to the color of candlewax, not fever which made his hands shake so badly that he almost dropped the decanter of brandy as he brought it out of the sideboard.†
Chpt 2

with a vengeance = with intensity
The eye of the outside world, which had slipped away from the Dragon Lady these last few years, had now returned with a vengeance.†
Chpt 3 *

Definitions:

(1) (vengeance as in: vengeance is mine)
the act of taking revenge

(Revenge means to harm someone to get them back for something harmful that they have done.)
(2) (with a vengeance as in: with a vengeance)
with intensity
(3) (meaning too rare to warrant focus)