Is there any way to search for giveaways with multiple copies of the game being given?

as far as I know , no. But have you tried the extension?

Use Steamgifts+. Its invaluable.

Steamgifts+? Could I get a link to it please?

Seeing as you're new here, here's another good link. It contains the site rules and regulations, and answers to many common questions / issues. Please take 10 minutes to read it.

I appreciate the link, tyvm.

And considering you're new at this, I'd also highly suggest you install Enhanced Steam. It makes using steampowered.com a lot better. It'll tell you pricing history, current and past bundles of specific games, and it'll link show you links for peoples Steamtrades, SteamRep, and Steamgifts accounts. Makes it trickier for people to try and scam you by impersonating someone else.

Using feedsifter with the SteamGifts RSS feed should do the job & does not require any additional browser addons. Keep in mind, it'll only show public giveaways - group giveaways you're eligible for will not show up.

Edit: I suck with markdown ;)

Use Steamgifts Plus. Very useful user addon.