In reply to Stone Muppet:
You could broaden your circle of climbing partners. then see if any of them are interested in an expedition.
Or you could ask here in the lifts and partners section for a partner.
Or you could go on a commercial expedition. Tom from Jagged Globe often pops up here (he has replied to the thread already) and I'm sure JG would be happy to have a conversation with you about options. There are other companies, too. If exploratory expeditions are your thing, then JG go to Ladakh, and you can also look at ISM (Tien Shan), Martin Moran (Himalayas) or John Briggs (Andes).
Of course, not all expeditions need take a long time.
You could go to the polar regions for a week or a fortnight. There are scheduled flights to Svalbard and to Greenland, and the altitude is not a problem. You might take most of your available time getting to and from the start of the route, but that is all part of the expedition thing.