This is a question I recently got, and the answer is simple: yes, but the maximum annual IRA investment is a total (cumulative) amount, not per account. In other words, if you have four different IRAs with four different companies and your maximum IRA contribution is $4,000 for the year, you can only contribute $4,000 total, to all four accounts.
A more important question is: should you have different accounts?
Most investment advisors will tell you no, partly because it will be too difficult to manage, and partly because they want all of your money to be going to them and their funds.
While there is more to pay attention to when holding multiple accounts, there is usually little active management that goes on in an IRA. You open the account, buy the securities (usually mutual funds or money markets), and hold.
There isn’t really a lot of management with an IRA. Every year you’ll want to make sure your asset allocation is appropriate. You’ll add funds as you can.
The benefit of holding multiple accounts is no different than the benefit of holding different investments: diversification. Maybe one company is offering low fees but has a limited selection of mutual funds available. Another company may have slightly higher transaction costs but a wider variety of funds.
Sometimes, opening a new account is the only way to invest in a mutual fund you really would like to hold in an IRA. If your current broker (or 401(k), or SEP IRA, etc.) does not offer a particular fund, for example, you may have to open an account with another broker just to hold a fund in a tax-deferred account.
The downside is cost… maybe
Each company you have an account with will likely charge you a fee for management, but some discount brokers only charge for purchases and redemptions. As a result, you should have as few accounts as possible.
So, take a look at account fees and determine whether it’s worth it to pay each company the fees it is deducting from your bottom line.
The important thing is that you are satisfied with your investments and the way the management company reports your holdings, returns and losses.