Are Time Machine backups to an external disk attached to a Time Capsule supported? My 1 TB Time Capsule drive is full with Time Machine backups.  I'd rather spend $130 on a 3 TB drive than $500 on a new 3 TB Time Capsule.

Is an external drive attached to a Time Capsule supported for Time Machine backups?  I have read that trying to use Time Machine with an Airport Extreme and an attached external drive is not supported and is in fact unreliable.  Does that extend to Time Capsules with an external drive?

I realize that a Time Machine backup cannot be split across drives -- I would move entire backups to the 3 TB drive.

I bought my 1st generation Time Capsule (MB277LL/A) in 2008. I am running Mountain Lion.
Yes. You can use Time Machine with a drive connected to a Time Capsule.

This Apple support doc - Backup disks you can use with Time Machine (as of Sept 2015) - says:


  Time Machine can back up the data on your Mac to these backup disks:
  
  
  An external USB, Thunderbolt, or FireWire drive connected to your Mac
  An AirPort Time Capsule's built-in drive (any model) 
  An external USB drive connected to an AirPort Time Capsule (any model) or AirPort Extreme (802.11ac model only)
  Network volumes connected using Apple File Protocol (AFP)