Okay, this may be something everyone does - but I just tried it and loved it.
We make eight day pickles at home (they take eight days) which are a type of sweet pickle. My wife prefers kosher dills, so she buys a jar every once in a while (this year we'll be canning our own).
I will note that I have no pickle preference - I am terrible at these types of choices in general. Anyway...
I was out of sweet-pickles. But the jar of brine was still half full. What to do? Well, my wife had some kosher dills that weren't the right brand for her (she is pregnant, and also picky - a fateful combo!) so I pulled out the dills and put them in the sweet brine.
AHHHHH! SOOO GOOOD! The resultant pickle was salty and sour and sweet. I am sure there are many a recipe to produce such a pickle without the swapping, but I will tell you if you're ever in the mood, do some pickle swapping. Fantastic.