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Yes you can have both a SEP and a 401(k) but there is a limit on the combined contribution amount. If you used the IRS Form 5305-SEP to establish the plan, then you cannot fund a different type of plan for the same year as the terms of the agreement prohibit this. You would need to revise the plan with a prototype SEP document in order to also have a 401(k) for the same year. Some mutual fund groups and brokerage firms have SEP prototype documents.
The primary difference between the plans is the SEP only permits employer contributions whereas the 401(k) permits both employer and employee contributions (via salary deferrals). In a 401(k) plan, you could defer up to $18,000 ($24,000 if age 50 or older) from your W-2 and the S corporation could contribute up to 25% of your W-2. You would also need to make employer contributions for your employee if there are employer contributions made for yourself (some flexible funding strategies are available to reduce the % for your employee if you wish). The SEP permits employer contributions of up to 25% of W-2 amounts. So your S corporation could contribute up to 25% for you, not 20%. If you have both plans, then the total employer contributions are 25%, not 25% to each plan. However, the 401(k) plan would also permit you to reduce your W-2 via employee deferrals.
A 401(k) plan is much more complex to administer than a SEP. You would need to comply with a number of DOL and IRS regulations and file a Form 5500 each year. Some small businesses who sponsor 401(k) hire administrators to do this work (usually $1,000 to $1,500 for small employers). It is too late to establish a 401(K) for the 2016 tax year.
Below are some links from the IRS with Q & As.
Yes, the S corp could contribute up to 25% of your W-2 as a profit sharing contribution. However, that is part of the 25% employer deduction limit. There are some exceptions that would permit you to contribute more than 25% for yourself and less for your employee so that the total S corp deduction would not exceed 25%. For example, if certain variables (such as employee is significantly younger than you) apply, then you could possibly only be required to contribute 5% for your employee and you could receive a contribution of 30 - 31%. In order for this to happen though the plan would either have to be designed as a cross-tested (new comparability) plan or be integrated with social security. Since this type of plan is more complex, an administrator would be needed and the total costs to administer the plan would be $2,000 - $2,500 annually.
I am assuming that your S corporation pass through income to you is sufficient to take advantage of employer contribution deductions.
A type of plan that would permit much larger employer deductions would be a defined benefit plan. This is often used in conjunction with a 401(k) plan to maximize deductions. The maximum contribution and deduction would be an amount that would permit you to fund a plan that would provide you with an annual retirement amount equivalent to your average 3 highest years of income. This is the most complex type of plan and would require the services of an actuary. Here's a brief summary of the plan - http://www.investinganswers.com/financial-dictionary/retirement-planning/defined-benefit-plan-2025