I've purchased the first party upgrade, and I cannot figure out how to add another sylvesti to my party. I have been offline for a while, is there a button I'm supposed to hit to add that extra pet?

go to party page
scroll to the paired dropdowns and use them to select the pet you want to add to the party (left = stable selection, right = pets in that stable)
once the pet has loaded in the display (shows the first pet in your stables by default), hit the green + that's next to those dropdowns
the pet will be added to the party display- you can then click on the pets' party display boxes to swap them around (like when rearranging items in the inventory)
Once you're happy, click the Set Party button to save the changes

:) Thanks.