If you're current running on a /24, you want to define other subnets for what purpose?
Reason I ask, as others have mentioned, you can NAT to Arris cable modem, however, low end Catalyst switches generally don't support NAT. As others have also mentioned, low end Cisco routers do support NAT, but you might find their NAT support, if you need to use PAT, might not work as well as what the Arris cable modem supports. Further, low end Cisco routers generally do not have high bandwidth capacity. I.e. you might find your cable modem's throughput is limited by the router (such as a 2811).
In other words, what you might do, and perhaps what you should do, may have different answers, especially if cost is considered. (I.e. whether you need to buy more powerful equipment.)
If a low end Cisco router presents itself to the Arris cable modem as a single host, or hosts, on the existing /24 network, it should work, again though, you might find presenting all your internal hosts as a single host might break some applications. If you don't use PAT, but just use a pool of NAT addresses, that is likely to work best, but you then need to consider whether a /24 is a sufficiently large NAT pool.
Rick raises an interesting point, i.e. whether the Arris cable model supports more than one internal side network. Likely not, but as Rick notes, if it does, that would be a solution. As far your ISP is concerned, doubtful they concern themselves with what you do on the internal side of cable modem, beyond your bandwidth consumption.
