"plenty of times" is correct and usable in written English. You can use it when referring to a number of times that something has happened. For example: "I've seen that movie plenty of times."
TM: Plenty of times!
"He's terrorized me plenty of times.
Plenty of times, you get skunked".
"Yeah, there have been plenty of times.
"Plenty of times," he said.
We've all seen it plenty of times".
I'd chickened out plenty of times, too.
I've been knocked off plenty of times.
He has said so plenty of times.
He will walk plenty of times".
I've done this plenty of times.
I love the desktop app, it’s always running on my Mac. Ludwig is the best English buddy, it answers my 100 queries per day and stays cool.
Cristina Valenza
Retail Lead Linguist @ Apple Inc.