In theory, it should work: 9.x to 9.3, then 9.3 to 11.0. I don't even know whether the 9.x upgrades can still be found, never looked.
In practice, you need to think about the following: How much work is it going to be? How much risk is there that in the middle of this giant leap (you are jumping several year's worth of development) something breaks, like one of the applications you (or your customers) can't live without?
Consider this alternative: Inventory exactly what your machine is being used for (you should know that anyhow, if you don't know it yet, learning it now is a good idea). Then start with a virgin disk, and install 11.0 (or the version of your choice), and then install all the necessary applications, test them carefully, and then replace the existing 9.1 system with a new 11.0 system. It also allows you to perform the setup of 11.0 really neatly (do it the way you really want, not carry old hacks from a long time ago with you), and think about design choices in how you configure things.
It's a tradeoff, and in the end, you need to make that tradeoff based on your estimates of the resource requirements, and the quality of the resulting solution. I had a similar problem (having to go from a 9.0 system that had never been upgraded at all to 11.0), and decided to do the giant leap with setting up a new system. That was easy for me, since the server in question just runs a household (with some machine control functions), and I had time over winter vacation to switch it around, I had enough spare machines and spare disks to perform the setup on, and I could afford the 2 hour downtime of the actual transition. YMMV.
