As long as all of your pre-tax money is in a 401K you can do the back-door Roth. If you have funds in a traditional IRA it won't work.
So basically you set up a shell IRA in which you make a
non-deductible contribution up to the max annual amount. You then can immediately convert the non-deductible contribution to a Roth. This zeros out the IRA again. You never claim the deduction so the funds you convert to the Roth have already been taxed. People above the Roth phase out range do this all the time.
The reason why it won't work if you already have an IRA with a balance is because the conversion to a Roth is not LIFO, it's based on the percentage of your IRA balance.
For example, if you have an IRA with 45K in pre tax funds and add 5K as non-deductible to make 50K total, the IRS will not let you simply covert the last 5K that was non-deductible. They'll look at the percentage of non-deductible to deductible. So in that example only 10% of your conversion will be tax free. The remaining 90% will be taxable in the conversion.
Remember the IRS considers all of your IRAs to be one so if you have one anywhere with a balance it will be considered in your conversion.
Bottom line, don't try to do a back door Roth if you already have a traditional IRA with a balance. Make sure to loop in your tax advisor or research your situation as I am not a tax advisor.
@Ouchie-Z-Clown Can you verify the above?