Create a mail template for each company profile. Could be just a field for text that appears above the download link.
The current workaround is to manage companies under separate accounts and use this tool: https://www.billiving.com/accountant
Michiel Klonhammer commented
For us this doesn't work, as that would take logging in for every other invoice (to switch languages for the message etc). For now it's ok to copy some text from an external document, but it would work better if each company profile had it's own message.