I go to Brown, not Penn; but I believe you’re referring to sub-matriculation, which is mainly for Masters degrees, though there are some professional degrees offered (which obviously take longer than 4 years.) You usually apply in your Junior/Senior year to sub-matriculate, though there are some dual-degree programs that build this into their curriculum (Seven-Year Bio/Dental, Vagelos Molecular Life Sciences etc.) You’ll likely have to apply as a HS Senior in-order to participate in the coordinated dual-degree programs, so make sure to take a look at the Admissions Website (linked below.)
Here’s further information from CAS about the program and the participating departments: https://www.college.upenn.edu/submatriculation
Peen Dual-Degree Programs: https://admissions.upenn.edu/learning-at-penn/major-minors/earn-multiple-degrees
Sub-matriculation is not for the faint of heart: it’s a serious commitment and I would highly discourage you from contemplating a double-major, a minor, AND a Masters to boot. IMO choose a singular major, the Masters, and potentially the minor if you have free electives and feel like the work is manageable.