Is the cap of seven sacraments dogmatic?

Is it possible for there to be, at some future time, more than the current seven sacraments administered through the Church?

No, there are no more sacraments to be declared. As the Council of Trent stated:

Canons On The Sacraments In General

Canon 1. If anyone says that the sacraments of the New Law were not all instituted by our Lord Jesus Christ, or that there are more or less than seven…let him be anathema.

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