I just answered a question on www.Nerdwallet.com which was "You can have a Traditional IRA and a Roth IRA; but can you also have a 401k and a Roth 401k, all 4 at the same time?" and thought I'd put this on my blog since it is a common question. Here is my answer:
Yes, you most certainly can have a Traditional IRA, a Roth IRA, a 401k, and a Roth 401k all at the same time. The issue will be which you can contribute to and how much.
For example, the annual contribution limit for IRAs is $5,500 plus $1,000 catch up (CU) if over 50. Let’s assume you are under 50 for my explanation. You can contribute any combination of amounts between a Traditional IRA and a Roth IRA as long as the total does not go over the limit, $5,500. So you could put $3,000 in your Traditional IRA and $3,500 in your Roth, or $1,000 in your Traditional IRA and $4,500 in your Roth.
Anyone can contribute to an IRA regardless of income but your ability to deduct it would be limited if your Adjusted Gross Income (AGI) is over $98,000-$118,000 if you file a joint tax return ($61,000-$71,000 Single/Head of Household) being that you are covered by an employer plan. If you make too much to make a deductible contribution then you might want to look to the Roth IRA however your ability to contribute to a Roth IRA is limited if your Modified AGI is $184,000 to $194,000 for joint filers ($$117,000 to $132,000 single/HOH). If you are over this amount then you would consider a non-deductible IRA and potentially convert it to a Roth (no income limit to convert) supposing you have no other IRA funds (if you do a pro-rata rule applies and may not be worthwhile).
The 401k contribution limit is $18,000 with a $6,000 catchup if you are over 50 (which I’ll assume you are not for purposes of this answer). Similar to the answer above on contributing to a Traditional IRA and a Roth IRA, you can contribute to both your 401k and your Roth 401k as long as the total does not go over $18,000. The amount you contribute to the 401k or Roth 401k has no impact on the amount you can contribute to an IRA (but does affect whether you can deduct it or not).
So if you have the money you can put $5,500 ($1,000 CU) to any combination of IRA and Roth IRA plus $18,000 ($6,000 CU) to any combination of 401k and Roth 401k for a total of $23,500 ($30,500 if over 50).
Now whether you should put more in the pre-tax versus the Roth (tax-free) is essentially a function of what your marginal tax bracket is now versus what you think it will be when you take the funds out. If you think you will be in a lower bracket in the future then pre-tax is the way to go, however if you think you will be in a higher bracket and/or you think tax rates are going up (due to terrible government debt) then Roth can be the way to go. If you’re not sure you can diversify to both which is not a bad idea. The pre-tax vs. Roth is really like any other investment except that you are betting on tax rates. One will be better than the other but you won’t know until the future arrives which is the same reason we diversify between stocks and bonds, between US and international and emerging markets, and Large cap and small cap, and growth and value, etc.