That's a good strategy to for small kids. The language of the environment (friends, school, TV, games, movies, sports) will win in the long run, so you really don't need to do anything to support this unless you see some unusual problem.
Having each parent talk a different language will be good in learning the basics of the spoken language and developing accent free pronunciation. At some point, when you start talking in "A" the kid will start replying in "B", since it's easier. You need to think carefully on how to react to this and be consistent about it. "Sorry, I only speak A with you. It's important so both of us can have our special language". Pretending that you don't understand is silly, so don't. If there is a grandparent or other relatives that are important and don't speak "B", you can use them as an argument.
When the kids get older, reading and writing becomes an issue. Reading is pretty straight forward and can be supported by getting lots of books in the non-B languages, doing story time, etc. Writing, on the other hand, is hard. Learning to write will require some formal instructions and, if it's important, you need to budget time and classes for it.
Schools can be a mixed blessing: if the school teaches one of your non-local languages, check the quality of the instruction. In our case, the American high school offered German, but the teacher had a truly awful accent and his grammar was mostly wrong. This did more harm than good, so we pulled the kids out of this class and enrolled them in a accredited on-line course. Spanish, on the other hand, was excellent with native speakers and very good immersive instructions.
Another potential pit-fall: use it or you lose it. As the kids grow up, they spend a lot of time with a single language. Contrary to common believe, the unused languages do regress substantially. That happened to my oldest in college. I recently saw friends whose kids used to be fully fluent but after moving and 10+ year of little use, they lost at least 90% of their English.
We ended up with one bi-lingual, one tri-lingual and one almost 4-lingual child. The difference was really due to exposure to situations and environments where they could use the languages in a "natural" way. The more that happens the more they learn and retain.