I would highly recommend REI Adventures. We have used them for several hiking trips and are going on another next month.
Here is their Patagonia multi-sport trip:
https://www.rei.com/adventures/trips/latin/patagonia-hiking-cycling-kayaking.html
We actually chose a different company (MT Sobek) for Patagonia, as we only wanted to hike. We loved Patagonia; the mountains are stunningly beautiful and the people are welcoming.
REI does other multi-sport trips, including Croatia. You can probably filter for them on their website.
Also check Active Adventures, a New Zealand-based company, for trips in Europe and South America.
Their
Dolomites trip includes hiking, cycling, and a via Ferrata.
https://activeadventures.com
I doubt you will find any tours that offer rock climbing or ice climbing, as those are highly specialized and technical, and they would have to screen very carefully for experience and ability. And carry lots of extra insurance.
I believe are guide services in Alaska that will take you for a bit of ice-climbing as part of a semi-private group, specifically at Exit Glacier in Seward. You could “build your own adventure” by combining that with the ranger-led hike to Harding Icefield on another day, and then two nights at Kenai Fjords Glacier Lodge for sea kayaking at the face of Aialik glacier, with icebergs. Then head to Girdwood for some white-water rafting on Glacier Creek and more hiking, or rock or ice climbing.
Girdwood (home of Alyeska Ski and Summer Resort) is pretty much “adventure central” for Alaska. Here is a list of activities and adventures they put together. Scroll down to page 8 and later for white-water rafting, sea kayaking, ice climbing and rock climbing.