Tivos work with all cable boxes, as well as current small-dish and some large dish satellite setups.
The biggest drawback to the current Tivos is that they can only record one channel at a time while you're watching that same channel. Now, you CAN watch already recorded things while it's recording something, but you just can't change the channel in the middle of recording. Tivo will politely inform you of this when you try, giving you the choice to stop recording.
NOW.. Here's where it gets interesting. A new feature is called "multi-room viewing". If you have two or more Tivo 2 units, you can have each record different things (more than one channel recorded at a time) then share videos across your home network.
The big problem here is that when the Tivo was designed, adding a second tuner (which would require a second cable box) to the hardware was prohibitively expensive. At $49.00, adding two Tivos to your house shouldn't be terribly restrictive if you require a way to record multiple channels at the same time.
Regarding the possibility of installing a larger hard drive, you absolutely can, and it's actually fairly rare to find a Tivo which hasn't been expanded in some way. While Tivo obviously cannot officially support hacked boxes, adding hard drives, as well as most hacking is in fact quietly approved of by the company. The only thing they don't support is hacking into the subscription protocols, since that's really where they make their money rather than hardware.
Essentially the Tivo is a closed-ended Linux box. People are always doing things like increasing the memory, adding software features, memory and hard drives, etcetera. The only thing I really haven't tried is putting on a keyboard.
I have one series 1 which was hacked with a 40 gig drive (when 40 gig was the largest you could get) replacing the original 9 GB drive and one series 2 with a 60 gig drive which was bought direct from Tivo as a refurb (same type program). The only difference is, I paid, I believe, $200 for my existing Tivo2.
Check
http://www.tivocommunity.com/tivo-vb/ for more things on hacking.