@darkminir - ok so first, having multiple machines connecting through the same home "router/modem/gateway" - WON'T give you multiple IP's, they all have individual "internal" IP's on YOUR internal network, but as far as YouTube is concerned, they'd all be the same IP, so running multiple machines from the same location, like you mentioned wouldn't help anything.
That being said, I know a lot of services do exactly what Batoska said below... So if it's a concern, watch out for this - See his post - listed again below this sentence.
Don't use proxy or VPN for youtube, in most cases they are flagged and you can easily lose your account
Use your own IP , youtube allow the use of multiple account,just don't break their TOS and it will be fine
That being said, I DO know that some ISPs (Internet Service Providers) will "sell you" additional IP's from their allocated range for a low extra monthly cost. For example, I currently use DSL and my ISP will supposedly sell me additional Public IPs for under $10 a piece, per month. Since I haven't had the need to utilize something like this (yet), I haven't looked into how they would route through my gateway.
The VPS rental might be the best option, but I don't know if those would get flagged, similar to some proxies or VPN providers that have been flagged by other "services".
So - all that having been said, I don't know if YouTube does any of this (flagging IPs or ranges), but other different types of services have definitely done so, to a differing degree, in the past - maybe with YouTube, it's not a problem, I don't know. I'm not discussing or mentioning what they DO, but what they COULD POSSIBLY DO - big difference!
I don't know what they currently DO, so YMMV. As a for instance, Paypal is an SOB, they track every last damn thing you do and also when you took a piss last! YouTube may be much different. AlthoughI've read some pretty crafty stuff Google has pulled when de-indexing sites, so...
Also, since I've previously thought about this topic myself, If you do go the multiple IP route, make sure you use different machines (or virtual machines routing correctly) and I'd personally use a burner phone for each account or each set of phone verified accounts. Just to keep things separate. As somebody else mentioned a VPS might be a much better alternative, depending on your needs, just to keep things simple...
But make sure you use different phones to verify the accounts, if you go through the trouble of doing all the rest, as technically they can tie all of the accounts together with ANY piece of info shared between them.
I definitely understand where you're coming from... Although I don't intend on breaking any terms of service, I just wouldn't want for some stupid shit to "pop up" and ruin an entire business I had built, when they disable 20 accounts or whatever, especially if it was fairly easy to prevent.
Best of luck!