If what you want to do is to have the 1120 return tagged to your business (instead of individual) client in QBI, you can use the Merge Duplicate Clients tool, which you can access by clicking on the gear icon and find under Tools > Merge Duplicate Clients.
On the left column is the QBO client you want to merge TO and you'd choose the client you want to merge.
If your individual client uses Link, you should make sure all the related documents have been downloaded and the responses backed up before the merge as those will no longer be accessible under the individual client's record and neither will your client be able to access the same in Link.
P.S. All three of Intuit's professional tax products are branded ProConnect. ProConnect Tax Online is the only one that's cloud-based and it's called PTO for short.
Still an AllStar
I'm confused. Do you mean a schedule C or some other type of business entity? In any case, I believe the answer is no, but it is subject to change based on more information including what software you are using.