There is an easy but non-obvious way to do this.
Assuming you've got Google sync set up, and you can see your one Google Calendar on your phone already, go to https://www.google.com/calendar/syncselect (it needs the www; it doesn't have to be on your iPhone). You'll see a list of devices you're syncing. Select your iPhone.
On the next screen, you can choose which of your Google Calendars you want to sync with your iPhone. Check the box next to the desired calendars, then hit Done or Save or whatever it says at the bottom.
Open iCal on your iPhone, and give it a while to sync, and you now should see all of your selected Google Calendars on your iPhone.
For some reason, you can't change the colors of the calendars on the iPhone, so I change the colors in Google Calendar to match what the iPhone picks.
There used to be a limit of 5 Google Calendars that you could sync to the phone, but they recently raised the limit to 25.
These same instructions apply to the iPad and iPod touch. I've got this set up on all my devices, and it works like a charm.
This is documented by Google here: http://www.google.com/support/mobile/bin/answer.py?answer=139206
Keyboard shortcuts: Mail has it's own keyboard shortcuts, which you may have to learn.
Alternate email addresses/multiple accounts: works fine. Don't know about plus-addresses.
Priority inbox: this is not supported.
Labels work, as does flagging.
Public calendars work in iCal.
Syncing is very easy to set up - via IMAP in Mail, and in Preferences in iCal. In Lion it's even simpler.
Yes, you add each account separately in mail. You can still visit them in any browser or device.
Best Answer
You don't need any third party app to add different calendars to the built-in app. Just open the iOS preferences, go to Mail, Contacts, Calendars and add another account of your choice. In your case, just add another Google account.