Can I contribute to a 457 plan? I already have a 401k from a previous job, but my current employer offers a 457.

If your employer offers a 457 then you can contribute to it. Since the 401k is with a previous job, you can still leave it there, but you can no longer contribute more money to that 401k.

I found the following which is as detailed a you may want.

Contribution Limits

If the 457 plan is the only one your employer offers, the limits are the same as with a 401(k) - a maximum of $18,000 in 2016 for those under 50 years old, and up to $24,000 for those 50 and over.

But here's the difference: If your employer also offers a 401(k) or 403(b) plan, you can contribute to both the 457 and the other plan. Moreover, you can invest up to the maximum in each account. In 2016, the limits are $18,000 in each type of account, plus catch-up contributions - so you could make a total retirement contribution of as much as $36,000 (or $48,000 if you are 50 or older). Investing the max in both is a terrific option if you're getting started saving a little late, or you just want to maximize the advantages of these plans (tax breaks and matching, if any).

Even if you’re not eligible for another plan, special 457(b) has additional catch up provisions in for workers three years from the retirement age (as specified by their plan) to stash an additional $36,000 if you haven’t maxed out your retirement savings in previous years.

Early Withdrawals

No. Unlike with 401(k)s and 403(b)s, the IRS won't slap you with a penalty on withdrawals you make before age 59 ½ once you leave the company. You will, however, owe income tax on all withdrawals, regardless of your age. So busting into a 457 plan early still isn't a good idea. Leaving the money to compound until you're ready to retire will leave you with a much bigger nest egg.