That’s very similar to a variant that my friends and I used to play in college, which made the game MUCH more fun. Basically, if you have multiple cards of the same rank (but not necessarily the same color), you can play them all as a group, as long as the first one you play would be a legal play for you. The last one you played is then left on top as the card the next person plays on.
Note, however, that you can NOT “go out” with a “stack”, because there has to be a chance for someone to catch you forgetting to say “Uno”. So if your hand is 5 8’s and nothing else, you can play 4 of them at once and say “Uno”, but not all 5.
With skips, this means that you can skip all the other players at once, even in a non-2-player game. If there are 4 players and you have 3 skips, red green and yellow, and a green 6, and it comes to you with a yellow card showing, you can play yellow skip-blue skip-green skip as a group, say “Uno”, then immediately play green 6. So it’s possible to just “go out” with no one else having a chance with skips (or, in a 2 player game, reverses), but not with just numbers.
With draw 2s or draw 4s, we also used the rule mentioned here were the person who would be drawing can play more of the same card to send the drawing forward. This leads to some interesting strategic choices. For isntance, if it’s just me and one other guy, and my hand is 2 draw-2’s and one other card, in normal uno, I’d auto-win (assuming the colors matched up right) by playing draw 2, then draw 2, then say “Uno”, then my other card. With stacks, if I am certain that my opponent has no draw-2’s, I autowin by playing my 2 draw-2’s as a stack (making him draw 4), then playing my other card. However, if I suspect he has a draw 2, I play my first draw 2 hoping to bait him into playing his draw2 on it, so I can then play my OTHER draw 2 on that. However, if he didn’t have any draw 2’s, me might draw one as one of his 2 cards, so my plan might backfire. Etc.
It’s WAY more fun than normal Uno.
As for scorekeeping, if we had 5 players, we’d start with all 5 players and play until only one person was left with cards. That person would be out. The other 4 players would then start again and play until someone is out. Repeat until only 2 people are left. They play. The winner of that then gets one “point”, and we start over again with all 5 players.