Dublin Fire Brigade was called to Belcamp House in the north of the city in the early hours of Friday and again overnight into Saturday.
The Georgian mansion was designed by Kilkenny native James Hoban - architect of the White House in Washington DC.
Belcamp has been significantly damaged by fire and vandalism in recent years.
The site, off the Malahide Road, was formally used as a secondary school - Belcamp College - but was sold for development in 2004.
Dublin Fire Brigade deployed five units to the site early on Friday morning and a further three units overnight into Saturday.
A spokesman said it was too early to say what had caused this week's fires.
An Taisce (the National Trust for Ireland) had previously included Belcamp on its list of buildings at risk and it assessed it to be under "critical" threat.
Following the first fire on Friday morning, An Taisce wrote to Fingal Council urging the local authority to "take urgent action to protect the 18th Century house".
"This morning's fire has caused serious damage to the ornate plasterwork decorated interiors, which are the finest of the late 18th century period in Fingal.
"The extent of damage is still undetermined," the trust said.
An Taisce claimed the building had been "inadequately secured" following the Irish property crash.
It called on the council to "urgently intervene to establish the current ownership of the building and any continuing involvement of NAMA (National Assets Management Agency) and to ensure that the roof is repaired and further damage averted".
A historic Irish building, designed by the architect of the White House, has been damaged by fire for the second night in a row.