second-tier; mid-tier; sub-major
Used mainly for companies or organizations that are just below the top tier in size or influence, often in business or industry rankings.
That company is classified as a second-tier firm.
I got a job at a mid-tier securities company.
Compound of 準 (jun, 'semi-' or 'quasi-') and 大手 (ōte, 'major company'). The reading おおて is a standard kun'yomi compound.