The investor filed a lawsuit in a local court at the end of April against local financial company Jysan Ventures after it took over telecommunications firm KazTransCom and forced out minority shareholders.
Jysan Ventures has dismissed allegations of unfair practices as "unfounded" and said it abided by the law and bourse rules.
The investors allege the company used vague squeeze-out rules to force them to sell at artificially low prices. The fair price was at least 39% higher, they say, seeking compensation.
Bakht Niyazov, a private equity and venture investor, is among the plaintiffs.
He won a protracted legal battle against another local telecom firm, Kazakhtelecom, in 2019.
Niyazov said his campaign for minority rights was in part driven by concerns about his own business.
"The worse the situation is with investor protection in Kazakhstan, the harder it will be to develop our main projects linked to growing young companies," he told Reuters.
At the same time, the Qazaq Association of Minority Shareholders (QAMS), a lobbying group set up by activist investors, is pushing through legislative reform that would clarify squeeze-out rules and ensure minority investors get the same price as those selling majority stakes.
QAMS head Daniyar Temirbayev told Reuters the group has managed to get the authorities' attention by moves such as challenging the flattering assessment of Kazakh corporate governance regulations in the World Bank's annual Doing Business report - which Kazakhstan has long used as a benchmark.
The oil-rich former Soviet republic's equities market remains underdeveloped with very few liquid stocks and no meaningful foreign investment in local securities except for those listed abroad.
Offering hope of greater diversity, President Kassym-Jomart Tokayev ordered the government this year to resume the so-called "people's IPOs" where shares in privatised blue chips are offered exclusively to retail investors.
(Reporting by Olzhas Auyezov; editing by Jason Neely)