How can I run redis on a single server on different ports?

Launch redis-server and supply a different argument for 'port' which can be done on the command-line:

edd@max:~$ redis-server -h
Usage: ./redis-server [/path/to/redis.conf] [options]
       ./redis-server - (read config from stdin)
       ./redis-server -v or --version
       ./redis-server -h or --help
       ./redis-server --test-memory <megabytes>

Examples:
       ./redis-server (run the server with default conf)
       ./redis-server /etc/redis/6379.conf
       ./redis-server --port 7777
       ./redis-server --port 7777 --slaveof 127.0.0.1 8888
       ./redis-server /etc/myredis.conf --loglevel verbose

Sentinel mode:
       ./redis-server /etc/sentinel.conf --sentinel
edd@max:~$ 

You can do this from, say, /etc/rc.local as well so that this happens at startup.

But maybe you can also rethink your approach. Redis is so good at handling writes that you may just get by with a second database?

Very easy command:

echo "port 4000" | redis-server -

echo "port 4001" | redis-server -