The move comes after previous overtures at 143p were overwhelmingly rebuffed by the contractor’s shareholders.
Cathexis’ new cash offer of 171p a share represents a near 20% increase on the initial approach from the US investment firm, which already holds around a 30% stake in ISG.
Its new bid values ISG at £84.6m and is a 40% premium to its closing price on December 10, the day before the first offer was made.
Cathexis said this would be its final offer and gave shareholders until 17 February to take a decision.
ISG’s board led by chief executive David Lawther has consistently urged shareholders to reject Cathexis, brand the previous approach opportunistic and undervaluing the business.
Last week ISG said trading at its fit-out and engineering services businesses would outperform and exceed board expectations for the half-year when interim results were unveiled in early March.
But it also warned the costs of closing out certain remaining UK construction contracts entered into during challenging tendering market conditions between 2011 and 2013 were expected to rise by an “offsetting amount”.
ISG said its turnaround plan was on track with all but three of the 360 contracts entered into during this period now complete on site.
The firm’s order book at the end of the year stood at £1.1bn and the board underlined its intention to pay an interim dividend.
The half-year trading statement said: “Overall group trading results for the financial year ending 30 June 2016 are expected to be in line with the Board’s expectations following the pre-AGM statement on 1 December 2015.”