No, you should not have more then one Adsense account that is against the rules of Google Adsense. You can add more then 200 different domains in one Adsense account and if you have more then that you might be qualified for a Professional Adsense Account.

However if you are a webmaster in a company and they have one Adsense account and you have one private for your own website, that is not a problem. Just make sure that you do not ever log on the office account when you are home and vice versa. Google Adsense is tracking your logins and they might think you are having two accounts and might get banned.

If you want to track different websites with in your domain you can use something called Adsense channels

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