Robin Haynes Fisher, 44, reportedly fell ill while descending from the summit. An Irish man, Kevin Hynes, also died on Everest on Friday.
Nepal is facing scrutiny for issuing a record 381 permits, at $11,000 (£8,600) each, for this year's Spring season.
There have been reports of overcrowding and queuing climbers near the summit.
This week a photograph showing the tailbacks on Everest has been shared widely on social media.
Other deaths from this week include four people from India, one person from Nepal, an Austrian and an American.
A second Irish man, professor Séamus Lawless, is presumed dead after falling on the mountain last week.
(Excerpts from BBC News)