I have been to the BWCA now 6 times in the last 7 years.
I go with a friend of mine who has been there 3 to 4 times as much.
We typically try to go in and get away from the crowded areas, set up a base camp, and then take day trips out for fishing and/or exploring.

Our trip is usually 6 days (5 nights).

Is there a way, to legally have 2 sites (1 for just a night)

This is my thought. It might be a fun adventure, to set up base camp, and then 1 day, if the weather is good, taking a long journey out for the day, and maybe just tarp camping for the night at a different site. Getting up the next day and heading back to base.

The short answer is No...the long answer is No

That would be against the rules, one permit, one site. it would mess with the permit quota system and potentially cost someone a place to pitch their tent for a night.

I get what you are saying but it just wouldn't be a fair and ethical, not to mention legal practice.

Every year I paddle with three other guys. Two like to fish and two of us like to paddle and portage. Sometimes the two of us leave the base campers and do a long, long day trip but always get back by dinner or dark. We bring a tarp just in case but use the weather radio to ensure we don't get stuck by wind. It is a win win for all four of us.

Get a second permit and you can...

I think you now need to list all people on the permit when it is issued. I don't know if the FS would issue two permits to enter on the same day at the same entry point with the same people listed. I guess you could both get separate solo permits and then camp together at multiple places.

If you and your partner each pulled a permit for the same EP you would in theory be able to occupy 2 sites at the same time. However, pulling an additional permit just so you can take up 2 sites would be poor form in my opinion because it would prevent another group from being able to use that EP for that day. Blocking an EP's use just so you can occupy 2 sites on a single day just doesn't seem right to me.

I've done trips where we had multiple permits but it was for more substantial differences between the parts of our groups (entering and exiting on different days, partially taking different routes). I've also been thinking that this particular use seems a bit selfish.