How should I connect via DBD::Oracle to efficiently obtain 2000+ simultaneous connections?

I'm expanding, and adding extra web servers to handle my load. My
Apache/mod_perl environment maintains a new connection for each process, and
these processes seem to chew up a lot of server resources.

What is the normal acceptable way to maintain large numbers of simultaneous
connections?

I have enabled "shared server" support in my database, but I suspect it's
not being utilized, since I only get a few hundred connections before
hitting the "too many connections" error.

Am I supposed to be passing a switch in with my initical "connection"
requests to request a shared (instead of dedicated) connection maybe ?

Thanks all
- Chris.