Music videos are first and foremost about editing, so your first consideration should be your editing software and hardware, not the camera. AVID's Media Composer has a free version, but being free, it's obviously not as full featured; the most notable limitation for you is probably the lack of 4k support. But you don't need 4k now, anyway, especially since 4k also quadruples the computer hardware requirements you need (processing power, RAM, hard drive and external recorder capacity, data throughput/bus speed, etc.) And remember that when producing music videos, it's especially common to be cutting between multiple takes, so you're already quadrupling (for 4 takes) your computer hardware requirements (and/or quadrupling your render time). (You also don't need slo-mo for a music video, so you don't need a GH4, but I'm getting ahead of myself.)

But since you say money is not a problem, there's also Adobe Premiere and, if you're on a Mac, Final Cut Pro.

Your second concern for a music video is syncing multiple video tracks to an audio track. Plural Eyes is a decent low budget solution. Or you could buy a camera that supports time code.

And third, most (performance) music videos have fast (camera) movement and wide dynamic range, so you probably want a camera that can handle that. And that brings me to a Black Magic camera which is a far better video camera (with a global shutter) than a GH4. (And keep in mind that I've been shooting music videos on a GH1 since it came out in 2009 and currently shoot on a GH5 (and Canon 70D), so, if anything, you'd think I'd be biased toward them, but I'm actually recommending against them; primarily because you're not already heavily invested in m4/3 glass and you don't mention shooting stills /photos like I do.)

https://www.blackmagicdesign.com/

And as a bonus, Black Magic includes Da Vinci Resolve with their cameras. (I think all of them, but verify that, cuz like I said, I don't use Black Magic cameras.)

Also, if you really want 4k, Black Magic just announced a 4k Pocket Cinema camera at NAB (which I think uses the same sensor as the GH5S but in a much more video friendly package).