If you camp on the Canadian side of the border you have entered Canada. Regardless of how far you go across the border you are subject to a host of rules and restrictions that are totally different than staying in the USA in the BW. You would each need a Remote Area Border Crossing permit, subject to passing their criminal background check. About $30. Has to be done a couple of months in advance. You would need a Q permit at about $21 bucks a day per person, so 2 days each if you camp overnight. You would need a passport or card to re-enter the US and will have to use the new ROAM app to check back into the US. Free And, of course, you would be subject to various park and customs rules for Canada and the Q. Other than that it is easy.
There is a "Agnes Lake/Basswood Basecamp" permit that allows you to camp on the Canada side of Basswood or enter Agnes, but you are not supposed to use this to camp on any of the other lakes between Basswood and Agnes (Sunday for example) without going to Agnes first.