Using multiple hostnames on IIS

I have one website called Default Web Site on IIS that grabs all incoming traffic by using all unassigned IP address and omitting the hostname on the binding

So I can access it locally by going to the browser and typing in:

http://localhost/index.html

I can access it on another box in the Network, by opening up the browser and replacing local host with the machine name (webapps) like this:

http://webapps/index.html

That all works fine.

Now I've added a second website that uses the hostname intra.company.com in the binding for the site.

As mentioned in setting Host Name in IIS to www.example.com, I added the following to my hosts file located in C:\Windows\System32\drivers\etc

# localhost name resolution is handled within DNS itself.
#   127.0.0.1       localhost
#   ::1             localhost
    127.0.0.1       intra.company.com

Now, locally, I get the right page if I browse to:

http://intra.company.com/index.html

My question is, can I somehow navigate to that address from another computer, similar to how I was connecting to the site hosted on localhost.

Something like this:

http://webapps.intra.company.com/index.html
http://webapps/intra.company.com/index.html
http://webapps:intra.company.com/index.html

But none of those wild guesses at composing the url work.

Any Ideas?

Note 1: This might be resolvable through changing the DNS server on the network, but I can't access that for now, so I would like to see if there's a way route to a box plus a hostname.

Note 2: Also, I could add a virtual folder to the Default Web Site and redirect requests to localhost plus a folder name to the new website, but this feels like the wrong approach. I really do have two different websites that will resolve to different host names that have very different access patterns so keeping them separate seems ideal.