Opening the Manx Museum on two Sundays in July went down well with local residents and could herald further Sunday openings in future.
The Douglas attraction was opened specially for cruise ship passengers coming ashore.
Around 300 people went through the doors last Sunday, around a third of them locals.
Manx National Heritage bosses are now weighing-up the costs involved in seven day opening, but early indications are, it would be financially viable.
Entrance is free, so takings at the souvenir shop and cafe are crucial.
MNH Public Services Manager Howard Parkin:
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