The move is the latest development in an uneasy recent relationship between Elliott and Alliance Trust.
This past March and April, Elliott pushed for three new directors to be added to the board and met strong resistance within Alliance Trust, particularly from chair Karin Forseke.
Elliott ultimately all but won the tussle as mounting pressure and an impending shareholder vote meant Alliance Trust agreed to two of the nominees joining the board.
The raising of the stake does not necessarily mean there will be a fresh round of conflict but it suggests Elliott is not going to give up on whatever its plan is for the company any time soon, at least.
Something that is perhaps significant about the timing is that Alliance Trust has committed to unveiling new plans for improving shareholder returns this Autumn.
Shares in Alliance Trust are trading at 463p for a market cap of £2.557bn.