Currently, the pages trending/new/hot, show either a combined list of posts for all tags, or a list for one specific tag.
The URL https://steemit.com/trending
finds all trending posts regardless of their tags, while the URL https://steemit.com/trending/steemit
finds only trending posts with the tag 'steemit'.

Filter has one tag
However, the UI provides no way to see more than one tag, but not all tags at once.
A search for example with the tags 'steemit' and 'steem', that would return a list of posts for both tags, seems not to be possible at the moment.
My suggestion is to allow searching for a combination of multiple tags at once.
This would allow the user to monitor multiple specific tags at once instead having to visit each tag individually.
The tags could be separated with commas in the URL, like https://steemit.com/trending/steemit,steem
In the UI, a click on a tag could add that tag to the list of tags in the filter. For removal, a clickable symbol next to the tag could be introduced.
Double-click on a tag would search only for posts with that tag.
Maybe the number of tags in the filter needs to be limited for performance reasons.

Filter has two tags
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Wow, thanks. :)
Helpful advice.
Thank you @snug !!! Very useful post.
Thanks, @silbart. I hope so.
I like this idea. I think it would be very helpful to screen for all my separate interests. I know that not everyone I would like to see is already in my feed, but it's hard to check trending, new, hot across lots of different topics to find good content that deserves my 2 cents of reward.
This was also my thinking. It is really hard to follow topics without checking multiple trending pages at once. Actually I wonder if it would be possible to follow not only other users, but also tags. However, I can imagine that this would crowd the feed too much...
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This is completely necessary! I hope @steemit developers hear you!
That is so important. It is a realy urgently need. xD