Allow me to help answer some common questions about Chain missions as far as Standings Gains/Losses go, since those are questions that very few can actually give straight answers to.
1 - For regular mission chains (i.e. Recon 1/2/3 of 3), each individual mission counts as a separate mission with its own standings/ISK/LP value. Declining/Quitting these missions works the same way as any other regular mission: you lose 1x standing value of the mission upon Decline/Expiration after accepting and 1.17x that for Quitting.
2 - For storyline mission chains (i.e. The Sukuuvestaa Incident) which are only really still available from null-sec Pirate faction agents, it gets a lot weirder. The Faction standings are ONLY given to you for completing the very last mission in the chain, so you get nothing except the piecemeal Corp standings and ISK rewards for the missions leading up to that.
You will not lose standings for Declining any of the chain missions at any time, just like any other Storyline mission. But be very wcareful because if you Accept any of those missions and then hit that magical Quit button when you realize you aren’t interested in killing waves of Empire Faction rats or some jackass probes you and camps your site forever, you will still suffer the absolutely massive 3x Faction standing loss for hitting that Quit button, just like with any other Storyline mission.
Fortunately there is a way out of Accepted Storyline missions (especially chains) that doesn’t nuke your faction standings harder than if you’d killed a dozen Officer rats for that faction (yes, the hit is that bad): Letting any of the chain storyline missions except the last one Expire will not result in any standings losses. If you let the last one Expire, then you will suffer a much more lenient 1x Faction/Corp Standing Loss.
3 - Epic Arc mission chains are basically the same deal as Storyline chains (you get Corp standings for each mission, but only get Faction standings for the very last mission). However, you will not suffer ANY penalty EVER for declining or accepting-quitting any part of an Epic Arc mission, other than having to wait 90 days before you can restart the chain from the beginning as soon as you decline/quit any part. Epic Arc missions also never expire when offered or after being accepted, so you can take your time.
One big thing to note about the Epic Arc faction standings is that they do not concomittantly affect your other standings, unlike all other Faction standings you can gain in EVE. This property has some weird side effects as well, like the fact that you can actually fleet-share those Faction standings.
4 - COSMOS missions are one-time deals. As in, if you decline/quit/let expire any part of a COSMOS chain, you are locked out of that chain FOREVER. As such, you should be absolutely certain you can run these before you even go looking for the agents, whether you want to run these for the standings gains or the story modules/other loot. Failure shouldn’t even be an option with these.