@Adam_Collingwood. Having multiple “brand” websites under the same organization should not be a problem as long as there is not an issue with the automated response coming from the company your IS application is dedicated to. Unless the situation is each website represents a different company, then you’ll want to set-up an addition IS applications or other CRM as mentioned to captured leads independently.
I have a few clients that run multiple brand website, but everything still is captured and runs out of their Main/holding company through their single Infusionsoft application. In such a case, you can still use the Infusionsoft plugin across each website. If this is the case, I would suggest creating dedicated campaigns and forms to each website, you are capturing from.
Also, dependent on how you are using the IS plugin, there are also several other plugins that may resolve your issue as well. Check out FormLift, ninja forms, wpforms, gravity forms (still works for now) and contact 7, both have IS integrations. Also, check through integrations using Zapier or use the Infusionsoft form code to place on any of your websites. There are many out there to choose from.
Hope that helps and answers your inquiry. Wishing you great success!