Yes. A 401(k) is an employer retirement plan. An IRA is an individual retirement account. You are allowed to contribute the maximum allowed to both your personal retirement account and your employee retirement account. In 2016, you can contribute $5,500 ($6,500 if age 50+) to an IRA and up to $53k ($59k if age 50+) to a 401(k). You can always contribute to an IRA, but income limitations may mean your contribution cannot be deducted on your income tax return. This is called a “nondeductible IRA”.

Unless you can do a back-door Roth conversion, I would not recommend contributing to a nondeductible IRA. The reason? All growth and income in a nondeductible IRA is taxed at your top marginal income tax rate when you withdraw it. You would be better off with a “taxable” account as you will be taxed at lower rates for long-term-capital-gains and dividends.