Imagine ths situation: you are tax resident under NHR because you rented an apartment for the year and you spend 5 days in PT while the remaining 360 days you spend 90 days in 4 countries.
Put aside the fact that the other countries could claim you are creating a PE there, imagine that this wouldn't be the case.
Are you creating a PE in PT?
I agree it wouldn't sound very logical to have a PE in PT in that case but assumptions based on common sense are not necessarily aligned with what the law says. Check out the example of Greece:
For determining a legal entity as being tax resident in Greece, the exercise of effective management in Greece for any period during the tax year is sufficient.
Detailed description of corporate residence rules in Greece
taxsummaries.pwc.com
Again, I am not sure what the PT law says.
If the law of the country does not clearly establish a minimum number of days for effective management to trigger PE, I think there would be a significant risk of the company being liable to tax in that country if you spend time there.
Additionally, CFC could be a problem too for a US LLC not taxed in the US:
Detailed description of corporate group taxation rules in Portugal
taxsummaries.pwc.com
Profits or income derived by an entity resident in a black-listed jurisdiction, or in a jurisdiction where it is subject to an
effective taxation below 50% of the taxation that would have been applied if such entity was resident for tax purposes in Portugal, are imputed to the Portuguese taxpayer, provided it holds, directly or indirectly,
at least 25% of the share capital, voting rights, or rights on income or assets of that entity. Upon distribution of the profits, a deduction is available for previously imputed income.
I've both read that CFC rules in PT are applicable
a) to both active and passive income and
b) only if 25% or more of the company's income is passive
If b) is correct, CFC would not be a problem.
How likely this is to be enforced by the PT tax authority is another matter.