I wonder whether a user may have more than one "Hot Network Question” (HNQ) concurrently on one given SE site (i.e., >1 questions posted by the same user are HNQ at the same time in the same SE site).
Yes. The algorithm is ignorant of question authors. According to my script, on March 31st this year at 1:06am UTC, these two Travel.SE questions posted by the same author (guess who) were present in the Hot Network Questions list:
If we study the answer from David Fullerton on What are the criteria for questions to be selected for Hot Network Questions? we find the following exclusion rules for hot questions:
- Questions with no answers
- Closed questions
- Questions less than eight hours or more than 30 days old
- Questions that were already selected to appear on the list more than 72 hours ago
- Questions whose titles match a list of blocked keywords
- Questions whose titles contain MathJax markup
- Questions that a local moderator has manually removed from the list
- Questions on per-site metas, Meta Stack Exchange, Stack Apps, and non-English sites
None of those rules mention users. We don't care about those.