Individual schools will not need their own head teachers in future, with one person running several at once, a report suggests.
Heads say their workload is already too burdensome
The National College for School Leadership says deputies could look after each institution.
National Association of Head Teachers leader Mick Brookes called the NCSL's report "extremely unhelpful".
His union has warned that up to 500,000 children in England attend schools without permanent head teachers.
'A new era'
The NCSL report says schools should be put into larger groups under the control of one head teacher.
Several deputies could run one each for a few days a week.
Steve Munby, chief executive of NCSL, the government-backed training organisation for heads, said: "We are entering a new era in school leadership, which is challenging the long-held assumption that every school needs its own head teacher.
"In future school leadership may not be about just leading individual institutions, but about working in the wider system, although often still having one school as a base."
The research suggests the "system leadership" approach could offer a solution to recruitment shortages and offer new challenges to existing heads.
The NAHT has warned that up to 1,200 schools - or 500,000 pupils - are without permanent leaders.
It argues that heads' workload must be reduced to make the job more attractive.
Mr Brookes said: "Clearly in law every school does require a head teacher.
"To suggest that the answer to the overload of work that head teachers have is simply to delete the post actually beggars belief."
But Mr Munby added: "This isn't the cure-all for the recruitment challenge. It's just one of a range of possible solutions."