Hi, I like the circus rules you've got! I just used it for my first session, and it worked great! I noticed a few contradictions that I want to point out for you in case you want to tidy it up.
1. Under the Terminology -> Prestige section, you say the circus starts with Prestige 1. But in the Payouts and Prestige -> Earning Prestige section, you say the circus starts with Prestige 0.
2. On the first page, under Running a Show -> Excitement, you say that "if a great amount of excess excitement is generated you will critically succeed in the performance". But in the Payouts and Prestige -> Degrees of Success section, you say "in order to put on a critically successful show, the PCs must generate exactly as much Excitement as Anticipation."
I have a few other comments about the the Preparing the Show activities.
1. For the Circus Parade Success reward, is the Anticipation generated equal to half the character's level rounded down (as most things are) or rounded up (which is the level of the trick being performed during the parade)?
2. For the Practice Trick activity, you use the word "skill". I assume this activity should also be allowed to be completed with a saving throw or attack though, so the wording should be changed to allow for that. You could just say the PC Performs a Trick, like you did in the Circus Parade activity.
3. For the Practice Routine activity, you do not say what roll to make. I assume it is the same roll as Performa a Trick. Furthermore, the description says that the costarring PC gets the bonus, but the effects of a success and critical success say that the recipient of the Costar gets the success. Furthermore, if the costarring PC gets the bonus, it is unclear if the circumstance bonus applies to the Costar reaction's Aid roll or if it applies to their personal trick checks that have nothing to do with the costarring. Also, does the critical failure mean that the Costarring PC is not allowed to be a performer in the show, or that they just cannot use the Costar reaction with the PC who rolled the Practice Routine activity? Or is the intent that this activity must be used by the person who will use the Costar reaction? This activity is very unclear to me the more I think about it.
4. I actually have no idea what the Group Rehearsal (misspelled) activity is for. I guess it has nothing to do with Costar, since Practice Routine is already related to Costar. So the activity is just with some other PC or NPC? But there doesn't seem to be any interaction with that other character. It seems identical to Practice Trick. Are the circumstance bonuses of Group Rehearsal supposed to apply to the chosen PC or NPC, as if the person using this activity is auto-critically succeeds an Aid check, possibly granting the bonus that a person with legendary proficiency would give (+4)?
5. Are the circumstance bonuses from these activities supposed to apply to all of those trick checks in the show, or do they only apply once at the PC's choosing? I'm still pretty new to PF2, so I don't have a lot of intuition for these numerical bonuses yet.
6. Back to the Practice Routine activity. Since this applies circumstance bonuses, it is competing with the circumstance bonus from the Costar (Aid) reaction. Since the bonus of Practice Routine is larger than the bonus from Costar, I think this makes the Costar reaction obsolete, since bonuses of the same type do not stack.
7. In the Putting on a Show -> Act Success sidebar, you clearly define what it means for an Act to be successful, but I think you missed The Big Number. Is the Big Number successful if there are at least two successful performances, just like the Opener?
8. How would you feel about a critical success on a trick check counting as two successes for the purposes of determining whether an Act is successful or not? Seems reasonable to me.