I'm by no means an expert with Xero – a user only, but I can confirm that it is possible to set up your invoice templates to carry different corporate identification. In fact, that's exactly what we do when billing to different client groups.
Once set up (which I consider simple because even a bookkeeping klutz like me was able to do it), you need only select the appropriate template option at the time of billing.
You can certainly do this in Quickbooks Online (Intuit). You simply go the the invoice section and down at the bottom select customise and go ahead and set up your profile. I have clients who use three different invoice templates for three sections of their business. You can also divide up the invoices per each business by using classes on your invoices - this makes for great reports that are accurate & specific to each element of your business.
Not a Xero expert, but know this can be done easily with SAASU.