Q: In cases of a building that is several hundred years old and no date of consecration/dedication is known is it appropriate to dedicate the church after major renovations?
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A: A dedication of a church typically does take place after major renovations. This also applies to a cathedral. (In my diocese, the cathedral was built in 1883, but rededicated in 2003 after a major renovation, and that set the date when we now celebrate the solemnity.
Look at The Order of the Dedication of a Church and an Altar, Chapter III, The Order of the Dedication of a Church in Which Sacred Celebrations Are Already Taking Place, and you’ll see the criteria for this in the first paragraph. It looks for “something new or greatly changed” and requires an as yet undedicated altar.