The IRS does not have any restriction on the number of forms 1116 you can file. I have needed 2 for several years and my TurboTax returns have been efiled and accepted, though 2019 and 2020 were painful, taking several iterations each year due to TT limitations. You're up against TT's very poor programming on this topic, not an IRS restriction.
I won't be able to try to file this year for at least 2 more weeks as I don't have all my K-1s yet, so I can't help you with respect to 2021 status or any new ideas for resolving this problem.
