According to "Iron And Steel In 19th Century America: An Economic Inquiry" by Peter Temin, in 1867 a pamphlet claimed...
The cost of a plant with 2 three‑ton converters was given as $80,000; of a "five‑ton plant" with steam power, $125,000; and of first‑class apparatus with fireproof buildings and duplicate machinery making 50 tons of ingots in twenty‑four hours, $200,000. It cost only two‑thirds as much for a Bessemer plant as for a crucible steel, charcoal bloom, or puddled bar plant of the same capacity, the trustees asserted, and it took only 30 men to run a five‑ton Bessemer plant.
"The Albany and Rensselaer Iron and Steel Works, Troy, New York" by A. L. Holley is an excellent source. Holley licensed the technology from Bessemer and set up the Troy mill. His book, published in 1881, has extensive detail about the plant. It used three 7-ton vessels.
As the departments grew gradually and experimentally, and were not expected to exceed 60 tons of product per day, the buildings are not the size and arrangement that would now be made; but by means of convenient transporting apparatus, 400 tons of hot ingots per 24 hours are delivered by power into the blooming furnaces, and are rolled, cut up, and chipped, under a 7-ton hammer, and loaded hot on the rail mill cars with reasonable facility.
And...
Two copulas running together can melt 500 tons per 24 hours.
I'm no steel maker, but from reading Holley's accounts it seems the limiting factor was not the size of the converter but many, many others. He spends very little time on the converters and much more on blowing engines, pressure pumps, boilers, blooming trains (whatever that is), power feeding tables...
Troy had three 7-ton vessels in a mill able to deliver (not just melt) 400 tons per day. A single vessel would likely be less efficient. For example, with three one could be melting, one pouring, and one being cleaned.