It doesn't appear that the UI supports what you are looking for, as
Pinboard optimizes management of your personal bookmarks vs lots of
other people's.
However the API appears to allow the behavior you want by modifying
the url you call.
For example, you are searching for 'hottubing', first you click on
the
'Search All' button, which will then search other user's bookmarks and
take you to:
http://pinboard.in/t:hottub/
If you click on another tag like 'diy' in one of the found bookmarks
you'll notice it takes you to that particular person's bookmarks and
shows the ones that have that tag. This is the behavior you would
want if you're searching your own bookmarks, but if you want to see
everyone's bookmarks with 'hottub' and 'diy' then you can just add the
tag parameter to the URL in the address bar
http://pinboard.in/t:hottub/t:diy
So you can keep adding tags to narrow down your search and get more
targeted results. However keep in mind, that you are searching a
significantly smaller database on Pinboard vs Delicious, as the sites
are targeted at different user bases and have very different goals.
http://pinboard.in/about/
hope this helps.