Why storing the data on a SAN? What's the point? All database performance is tied to Disk I/O and you are using 3 servers with only one device for the I/O behind them. That makes no sense... and unfortunately so common.
I spend my life encountering poorly designed hardware platforms where people just try to design a large scale computer. All CPU power here, all disks there... hopefully there is not such a thing as remote RAM. And the saddest is they compensate the lack of efficiency of this design with huge servers that cost ten time more than they should. I saw $400k infra slower than a $1k laptop.
A SQL server software is a very advanced piece of software, it is designed to take advantage of any bits of hardware, CPU cores, CPU cache, TLB, RAM, disk controllers, hard drive cache... They almost include all filesystem logic. They are developed on regular computer and benchmarked on high end systems. Therfore a SQL server must have its own disks. Installing them on a SAN is like "emulating" a computer, you lose all performance optimisations. SANs are for storing backups, immutable files, and files you just append data to (logs).
Datacenter administrators tend to put all they can on SANs because this way they have only one pool of storage to manage, it's more easy than caring for storage on each server. It's a "I don't want to do my job" choice, and a very bad one, because then they have to deal with performance problems and all the company suffer from this. Just install software on the hardware it is designed for. Keep it simple. Care for I/O bandwidth, cache and context switch overhead, ressource jitter (happens when ressource is shared). You'll end up maintaining 1/10th of the devices for the same raw output power, save your ops team lot of headaches, gain performance that makes your end users happy and more productive, make your company a better place to work in, and save lot of energy (the planet will thank you).
You said in comments, you are considering to put SSD in your server. You will not recognize your setup with dedicated SSDs, compared to a SAN you'll get something like 500x improvement even with data and transaction log files on same drive. A state of the art SQL Server would have fast separate SSD for data and transaction log on different hardware controllers channels (most server motherboard have several). But compared to your current setup we are talking of sci-fi there. Just give SSD a try.