This is in the hands of your ISP. Unless your ISP change your IP, then no. As for COMPLETELY different, most ISPs are allocated a specific range of IPs, and therefore to get something completely different, you need to change ISPs.
Although most ISPs use dynamic IP, the lease times can be quite long. If you're on broadband, you may need to unplug the cable modem (possibly for as long as 24 hours) to obtain a new IP.
Alternatively, you could route all your connections through a proxy server.
Most people ask this question because their IP has been blacklisted in some way - in which case the best advice is to send a polite email to the sysadmin which blacklisted you.
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