The phrase “for more than a century” can be replaced by several synonyms that add variety and nuance to your language.
“For over a hundred years” is a straightforward alternative. It clearly states the duration of time being more than one hundred years. For example, “For over a hundred years, this family business has thrived.”
“For well over a century” emphasizes that the time period is significantly more than a century. For instance, “For well over a century, this landmark has stood as a symbol of the city.”
“For more than a hundred years running” gives a sense of continuous duration. It implies that the time has been unbroken. For example, “For more than a hundred years running, this tradition has been passed down.”
“For a span of more than a century” is a more formal and descriptive synonym. It uses “span” to suggest a period of time. For example, “For a span of more than a century, this institution has made significant contributions.”