"nearly at capacity" is correct and can be used in written English
You can use it when discussing levels of attendance, or when describing something that is almost filled to its limit. Example: The stadium was nearly at capacity for the championship game.
Today, traffic moves under the Hudson River through two 100-year-old tunnels that are nearly at capacity at peak travel times.
WeWork says that both units are nearly at capacity.
Toronto is sold out and Chicago and Detroit are nearly at capacity as well.
The venue was nearly at capacity, and with every member of the audience singing every lyric, Kerrang! magazine gave them a full page review in its following issue.
Despite the price decrease, Saudi Arabia has until now held off on decreasing its oil output, which is nearly at capacity.
With family homeless shelters nearly always at capacity, Billue does what he can, but sometimes that means providing only emergency food.
Employment is nearly at full capacity, and Canadian consumers have been spending big without triggering alarming default trends.
Currently, the company's North American plants are running at nearly 100 percent capacity.
Despite the favorable terms of the swap, Valero, for example, bought only one million barrels because, like most American refiners, it is running at nearly maximum capacity.
Fighter jets cannot, especially when defense contractors are already operating at nearly full capacity, says Gordon Adams, a national security expert who was part of Mr. Obama's transition team.
"Mount Morgan," which received positive reviews, has been running at nearly full capacity, according to Variety, but most of the tickets have been heavily discounted, selling for about $40, down from the top ticket price of $80.
