Chairwoman Lady Smith urged anyone with evidence to get in touch with the inquiry, even if they have already spoken to police or been involved in other investigations.
The inquiry is currently investigating seven boarding schools around Scotland:
-Fettes College, Edinburgh
-Keil School, Dumbarton
-Loretto School, East Lothian
-Merchiston Castle School, Edinburgh
-Morrison’s Academy (at the time it was a boarding school), Crieff
-Queen Victoria School, Dunblane
Lady Smith said: "In 2020, we plan to progress to case study hearings in relation to our investigations into abuse in boarding schools.
"We are interested in hearing from anyone about their experiences in boarding schools, particularly people who may have more recent experiences of having attended one of the schools currently under wider investigation from the 1980s up to December 2014.
"I would encourage anyone who has evidence to offer in relation to any of the investigations listed on our website to get in touch. We want to hear from you.
"I know that some people have already made a report to the police or to other agencies/persons and may have been involved in other investigations. That does not matter - please also talk to us."
Boarding schools will be the sixth phase of the inquiry and is expected to start next summer.
John Edward, director of the Scottish Council of Independent Schools, said in a statement: "The inquiry team has confirmed what was announced in 2015, that boarding schools would be looked at as part of the overall examination of school care accommodation.
"The schools have already worked with the inquiry team since the first announcement and have provided them with a substantial amount of detail.
"That full co-operation will continue through the hearings in 2020 and beyond.
"The safety and welfare of children at school is of paramount importance, and schools have zero tolerance towards staff who fail to live up to these values.
"The independent sector is no different from any other part of the school system in continuing to champion the highest standards of child welfare."
A further phase investigating foster care has also been announced for late 2020.
The inquiry is examining historical allegations of the abuse of children in care and began taking statements from witnesses in the spring of 2016.
The current hearings, phase four, focus on childcare establishments run by male religious orders.
These hearings are expected to conclude by late this year and will be followed by an examination of the abuse of children who left Scotland through the child migration programme.
The inquiry's witness support team can be contacted on 0800 0929 300, [email protected], or via SCAI, PO Box 24085, Edinburgh EH7 9EA.