IANAL, but it's my understanding that there's no particular conflict here. You'd be licensing the same work under multiple licenses; if any one of them authorizes some particular use, that's enough to be an affirmative defense against copyright infringement. If you violate the terms of one license, that particular license may become void, but as long as some others remain, you're fine.
In other words, licenses don't make certain uses of works forbidden; they make them _permitted_. If you license it under both GPLv3 and BSD, and someone does something permitted under BSD but forbidden under GPLv3, the GPLv3 can't forbid the BSD license.
That said, the current wording (the 'union of the terms specified' by all OSI licenses) is not multiply licensing, but something far stranger...
In other words, licenses don't make certain uses of works forbidden; they make them _permitted_. If you license it under both GPLv3 and BSD, and someone does something permitted under BSD but forbidden under GPLv3, the GPLv3 can't forbid the BSD license.
That said, the current wording (the 'union of the terms specified' by all OSI licenses) is not multiply licensing, but something far stranger...