eshell-number-of-handles

eshell-number-of-handles is a variable defined in `esh-io.el'.
Its value is

3

Documentation:
The number of file handles that eshell supports.
Currently this is standard input, output and error. But even all of
these Emacs does not currently support with asynchronous processes
(which is what eshell uses so that you can continue doing work in
other buffers) .

You can customize this variable.