The company, formerly known as Ortac Resources, has acquired a further 6% interest from Terra Metals in exchange for 17.5 million new ordinary shares of no par value in Arc Minerals.
It became Zamsort's largest shareholder in mid-May when it upped its holding from 14% to 49% by acquiring 35% of Terra's shares in Zamsort for 102.1 million new ordinary shares.
Arc also holds a convertible loan note in Zamsort, which can be converted into an additional 5.34% interest in the project's share capital.
It said it had applied for the 17.5 million shares to be admitted to trading on the AIM market, with admission expected on or around June 11.
This will bring the the number of issued shares to 556.5 million.
Arc executive chairman Nick von Schirnding said the move was another step forward in consolidating the company's ownership in Zamsort.
"We are very close to commencing the planned drill programme at Zamsort and look forward to a period of strong news flow for shareholders - both from Zamsort and Casa," he said.
The exploration activity will include 5,500m of diamond drilling and 6,500m of reverse circulation drilling, with RC drill results expected in the short-term.
The company's broker and nomad SP Angel said in a note it was "good to see Arc Minerals confirm its direct stake in Zamsort at 55% along with its option to go to 60.34%".
Th broker said it was looking forward to the results of the drill campaign and the production of copper and cobalt production sometime in the second half of the year.