Yes, totally. In fact it's quite common. I can't believe the exact figures but I believe it's about 20% of people with BP also have BPD and vice versa.
I have both and I can tell the difference between the two. Some people with both say they can't tell which symptoms are from which condition and that there is a crossover, but I can distinctly tell which of my behaviours of from which condition. A way to tell the difference is BPD is with you all the time, whereas the BP fluctuates and changes depending on whether you are stable, manic, or depressive etc. The behaviours you do all the time are caused by your BPD. The behaviours that change at different times are caused by your BP. This is just a general rule of thumb. But it's how I've made sense of it. Also, when you have BP with the correct meds you will notice a dramatic difference, whereas meds have little to no effect on BPD. The best way to treat BPD is with intensive therapy and DBT. the most effective treatment for BP is meds, therapy and a strong support network is a must. Just referring to what the last person said I think they misinterpreted your question. Either condition does not cause the other. They come from different origins entirely. BP is chemical and psychiatric and BPD is psychological and is typically triggered by a dysfunctional childhood. I hope I answered you question.