I am currently employed by a company that is an S-Corp and I bought in to the company to become 3% owner. They do not offer a 401K. I have a Roth IRA and a traditional IRA set up to backdoor into the Roth. Health insurance for myself and my family are paid for by the company. The health plan is not a HDHP, so it looks like a HSA is not an option. In addition to contributing to the IRA, are there any other tax advantaged accounts I would be eligible for?

I have cash in a high yield savings account and also have traditional investment account, so I am covered OK in that regard. A 529 is set up for kids' college.

You don't seem to be missing anything. The S Corp could have a retirement plan (SIMPLE, SEP, 410(k), etc), but the owners would incur varying levels of expense and administrative burden. There is up to $5000/yr credit (for 3 years) for the business if it implements a new retirement plan, so perhaps you could pitch that as an incentive to the decision makers.

As you probably know, any distributions you receive as an owner aren't considered earned income, thus not qualifying for any retirement account contribution.

You didn't mention if you are married but if you are and your spouse works, perhaps she has options that aren't being fully utilized?

Otherwise, appears to me that your best bet may be to focus on saving in tax efficient fund or funds, which won't save you any taxes today but should be favorably treated as capital gains later.

I don't know if you qualify or not but how about a solo 401K since you're technically an owner?

https://www.nerdwallet.com/article/investing/what-is-a-solo-401k

His W2 income would only qualify if the S Corp offered a plan for everyone. Any distributions he receives pursuant to his ownership isn't considered "earned" income and isn't eligible for retirement account contribution.

I am not married, so no spouse's fund to contribute to. Looks like I will just keep on keepin' on with what I have set up now.