Player count variants for Pitch
I'm an avid pitch player as well, 4pt 10pt and 13pt :)

For 2-3 players, you can play 4 point pitch with no teams! I find 4 point perfect for times when you need something to do but don't have a whole lot of time! You can also play 4 point pitch with 4 players, having 2 teams of 2 players. 

In 4 point pitch, the points are: 'High','Low','Jack','Game'. High being the highest trump card played (Ace usually), Low being the lowest trump played (two usually). Jack is the Jack in the suit that is trump. For 'High' and 'Jack' whoever takes these tricks and wins those points. For 'Low' whoever plays that card, regardless of who takes it in the trick it is played, will get that point. 'Game' is a sum of cards that you take in your tricks that you win. In any suit, Aces = 4pts, Kings = 3pts, Queens = 2pts, Jacks = 1pt, tens = 10 points. 'Game' can be tricky in this but it makes it interesting! Once all 6 tricks are finished, you add up the cards you took in the tricks to get your score for 'Game'. Whoever has the highest amount of points for 'Game' gets the single Game point.

In this game you play with all suits, but the first trick you still have to lead what you say is the trump suit. Minimum bid is 2, maximum bid is 4. You are dealt 6 cards and that is all you play with, the rest of the deck is not used and jokers are not used. Trump will win the trick if the other players do not play trump. If the first player of a trick plays trump, you must play trump if you have it (in other words, you must follow the first suit played, otherwise you can trump in at anytime or sluff off in a different suit if you cannot follow the first suit played). You can play to 11pts, 14pts, or 21pts.

For 6 players, you can play 10 point pitch which you explained in your post! The only difference, every player gets 9 cards and there is no deck left over. You play your hand with what you are dealt.

For 13 point pitch it is the same as 10pt pitch, you just play with with off 3 :) meaning if trump is hearts, the 3 of hearts and 3 of diamonds are both worth 3 points! so be very careful. You can play this with 4, 5, or 6 players.