Though Tommy Fleetwood is lurking menacingly, Højgaard moved into pole position on the back of a third-day 65 at Marco Simone Golf & Country Club in Rome, giving him the opportunity to create a slice of history.
After Rasmus won last week's Omega European Masters in Switzerland to become a three-time tour champion at the age of just 20, it would be the first time that brothers have triumphed back-to-back on the circuit if his sibling keeps his nose in front.
“Seeing Rasmus win is a big motivation," admitted Højgaard after moving to 13-under, one ahead of both Fleetwood (67) and South African Daniel van Tonder (66). “Hopefully I can get it done tomorrow."
Bidding to boost his hopes of hanging on to a top-tour card for next season, Scott Jamieson (71) sits on five-under, seven shots ahead of both Grant Forrest (73) and Calum Hill (75).
On the Challenge Tour, Euan Walker maintained his strong performance in the British Challenge with a third-round 69 at The Belfry. He sits in tie for fifth on 12-under, four shots ahead of Craig Howie (72).
In the amateur ranks, national champion Angus Carrick and Darren Howie were both nine-under for two rounds as they led Lothians and Borders respectively into the semi-finals of the Scottish Area Team Championship at Kings Golf Club in Inverness.
Lothians face Perth & Kinross in the last four while Borders are up against North.