Ares has a strong connection to bug spirits, and have even tried weaponizing them. It was also an Ares Firewatch team that caused the Cermac blast to begin with, essentially laying the groundwork for the liberation of the Chicago Containment Zone (at least to some degree).
Other potentials are the always opportunistic Aztechnology; they're into blood magic and who knows what else, so why not bug spirits.
That being said, any corp will do; they're all motivated by greed, so if there's something to gain they'll be taking their chances. Horizon is always looking for good PR, and cleaning up Chicago would be a massive publicity stunt. Evo is on the lookout for new gains in their major market of biotechnology. MCT and Renraku probably have interest in the corporate offices and research labs of other corps in Chicago, and S-K goes where the money is.
If I was doing a campaign like that in Chicago, I would probably focus on a few things. Recovery ops of information from the corps own offices (could be as simple as getting in, grabbing the optical chips/data terms that are still there, and fighting your way out); sabotage runs against [Humanis/The Horde/any other NPC faction the corp might have an issue with]; seek-and-destroy runs against specific bug spirit hives (this could be dangerous as all hell, so perhaps recon missions to start with.