how much does a connection cost?

The default config for max_connections is 32.

We have a server where we host web applications, each with its own
connection pool. For every additional webapp, I'm supposing that we are
placing more and more demands on those 32 connections (dividing a fixed
resource among increased clients).

So, it would seem to make sense to increase the max_connections whenever a
new webapp is created. However, what is the drawback to having more
connections available? Is it memory? disk space? file handles? Is there a
practical limit?

If anyone can lend their experience with this (and correct any
misconceptions ), I'd greatly appreciate it.

thx
andy