After you file

Thanks @dmertz   Im doing research and I have a hypothetical question similar to this situation, I’m hopeful you can help. 

let’s say this year I file my normal tax return in march 2025. In early April,  I notice that I missed something that increases my tax liability, but my return hasn’t been accepted yet. Since I know I shouldn’t file an amendment until the original return is processed, could I at least pay the amount I know I additionally owe online right away?  Would this make it so I don’t have to pay interest - Even tho the date I submit my amendment is after April 15th?  Or is the most important thing the IRS looks at the date of filing the amendment to if you owe interest?