I'm pretty sure the answer is no, but I will wait for @dmertz .
Anything you could have done about the 2022 contribution would have to be done before October 15, 2023, if anything was even allowed. And you can't make a new contribution for 2023 after April 15, 2024.
But I want to point out an alternative. Since you made a non-deductible contribution for 2022, and if this is your only IRA contribution so far, you can convert that to a Roth IRA now, and only pay tax on any gains (increase in value). Then, you pay no more taxes when you withdraw it during retirement. You could then make a deductible contribution to a traditional IRA for 2024, and go forward from there (I believe 2023 is a lost cause at this late date).
If you leave the non-deductible IRA contribution in the traditional IRA and add deductible money on top, you create a situation with mixed contributions in a traditional IRA that requires a lot of paperwork to keep track of on your end. It would be greatly to your advantage to convert the non-deductible funds to a Roth IRA if you can.
