  In 2004, Cs\"{o}rg\H{o} constructed a loop of nilpotency class three with
abelian group of inner mappings. Until now, no other examples were known. We
construct many such loops from groups of nilpotency class two by replacing the
product $xy$ with $xyh$ in certain positions, where $h$ is a central
involution. The location of the replacements is ultimately governed by a
symmetric trilinear alternating form.
