How about Tae Kwon Do and Shobudo Bujutsu Jujutsu? I have a 1st dan in the former and have only recently begun the latter, even though I do have some small prior experience in Hakko Ryu and a couple similar.
I find that while I could manage, just barely, to blend some approaches from Hakko Ryu into my TKD one-steps, forms and (at least theoretically, sparring) it does not work out with Shobudo. I am finding that they don't combine at all, that I am going to have to find a way of slipping fluidly from one to another and back.
It is the footwork which makes the difference. I could manage to do some few Hakko Ryu-ish things from a TKD stance. But Shobudo simply must be done from a Shobudo footwork perspective.
The engagement distance for Hakko Ryu was so close that TKD did not apply, so there was no real conflict. But Shobudo has mid-range engagment techniques which overlap TKD ones in scope and application. So one has to decide on the instant, which is best for this or that situation.
I really, really like having some grappling in my repertoir because, face it, striking is not always the best course either legally, socially or ethically. Many more occasions can be avoided or side-stepped. In-between ones can be met with a moderate amount of force. But once you punch or kick somebody, that's it. Count on the cops and lawyers to enter the fray at some point or other after that. Jujutsu can be applied subtly. Done with absolute skill it may not even look like anything much at all on a security camera playback. How cool is that.
Much as I approve of this concept. If there are two or more (which has never yet happend to me personally) then, in such event (hopefully never to come) all subtlety will have to be cast aside. TKD to my rescue then, for certain. But to handle any lesser situation, I'm hoping that my grappling may suffice.
That, anyway, is how I see them blendng together in my own, admittedly hypothetical, scenario.