This is straight from MN Law. Not every letter of every fish and game law is in the fishing rule book. Note Subpart 5C states that fish caught after a limit is reached must be immediately released. To me, that statement implies that fishing for the species that was limited out can still be targeted.
6262.0100 GENERAL RESTRICTIONS ON TAKING FISH.
Subp. 5. Possession of fish while on state waters.
A. Fish that are taken by angling and not immediately released into the water after capture are considered to be in possession. Once a limit of fish has been reduced to possession, no culling or live well sorting (the act of replacing one fish with another one) of that species is allowed.
B. A person shall not angle for, including catch-and-release, or reduce to possession any species during its closed season.
C. Once a person or persons fishing as a party as provided in Minnesota Statutes, section 97C.317, retain a daily limit for a species, all fish of that species that are subsequently taken must be immediately released into the water after capture.
§D. While on or fishing in state waters with size restrictions that differ from statewide regulations, including experimental waters, special management waters, boundary waters, or any other waters with size restrictions, all fish for which the different size restrictions apply must be undressed and measurable when in a person’s possession, regardless of where taken, except under the following conditions:
(1) when a watercraft is docked or moored to shore or when on the ice and a person is in the act of preparing and using the fish for a meal; or
§(2) when a person is on an experimental or special management water and the fish were lawfully taken, have been packaged and labeled by a licensed fish packer, are to be prepared for a meal while on the ice or shore of that water body, and do not otherwise exceed the statewide possession limits.
When fish are consumed under subitem (1), the angler must maintain the carcass of a fish with size limits in such a way that the carcass may be readily unpacked, unwrapped, and separated so that the carcass may be examined, measured, and counted to ensure compliance with size restrictions for that day, as defined under Minnesota Statutes, section 645.45.
E. It is unlawful for a person to have in possession, regardless of where taken, any fish in excess of or outside of the limits for that water body when fishing in that water. A person must immediately return to the water any fish that is taken by angling that is in excess of or outside the limits. This item does not apply to a person who is on an experimental or special management water and the fish were lawfully taken, have been packaged and labeled by a licensed fish packer, are to be prepared for a meal while on the ice or shore of that water body, and do not otherwise exceed the statewide possession limits.
F. A person who is in transit on the water, taking the most direct route back to the person’s lodging or docking, and not fishing, may possess fish outside of or in excess of the limits for that water body, if the species were legally taken from connected waters.