Competing Offer vs. Existing Company Offer

Hello all, I'm new to this subreddit and I had a quick question.

I should preface this by saying I have a feeling this is frowned upon but I wanted to get some outside opinions.

I've landed a solid offer from another company and my existing company is about to have me come back on (after being furloughed for a short while) as full-time. I'd like to present the competing offer to my existing company and see if they can exceed it, but the intent here is to use that to my own advantage. I would be looking to use that to present to the competing company and see if I can't get a slightly better offer.

Again, I'm pretty certain this is wrong. However, I don't have that much experience negotiating salaries so it's an honest question. Thanks.