Takashi Yamaya's Multiple from doujin publisher KUA seems to have been born along these lines. The number deck consists of four copies each of the numbers 0-9, the addition sign (+), and the subtraction sign (-). Players receive seven cards at random and place them face up on the table in front of them. Be the first player to rid yourself of cards, and you win the game — but you can't just throw the cards on the floor. Oh, no, you must get rid of them by creating multiples of target numbers.
How does this work? One player takes the mission deck, then reveals the top card, which shows something like "Multiples of 5". If possible, this player then creates a multiple of 5 using one or more cards in front of them, then discards those cards. You can use a single card (which isn't possible here), two cards to create a two-digit number (again not possible), or multiple single numbers that are connected by one or more addition or subtraction signs. Success! You have both 9 - 4 and 7 - 2. Which do you want to use?
If you can't or don't want to use your cards to create a multiple of the target number — which will be 3, 4, 5, or 7 — then you draw a new card from the number deck to give yourself something else that you need to discard. That's the opposite of progress, sure, but that's how games work, by making things difficult.
You can't create a multiple that someone else has already used for a mission, so if you have choices, look around the table to see who you can block. You also can't use 0 as a multiple, which seems reasonable given that while 0 is indeed a multiple of all numbers, creating a 0 to rid yourself of cards is lame.
A couple of missions force all players to draw a card, then the active player must draw a new mission. Anti-progress strikes again!
I've played Multiple three times on a review copy from Japon Brand, which will sell the game at SPIEL '17, once each with two, three, and four players. After playing, one of the players joked that it was almost a game, yet when we played again with someone who had just arrived at the game table, I did far better than I did the first time.
In the first game with two players, our number card counts bobbed up and down like corks on a wave, but in the second and third games I had an idea of which mission cards remained in the deck and I played to those probabilities. You can still be thwarted in that effort by the "draw a card" mission or the missions that prohibit you from using the addition or subtraction signs, but even so, you can play better than you did the first time. You realize that you can string together multiple signs to create a target, e.g., 8 - 4 + 1, or that you might want to save a 5 or 0 in case a "multiple of 5" card is revealed. Okay, you probably don't want to save a 0; they seem terrible, aside from making an easy 30, 40, 50, or 70, in which case they're golden.
I'm probably overthinking this, aren't I?