Bandwidth with SAS expanders and RAID controllers

Having a RAID controller that has eight internal SATA3 lanes, you can get 6 Gb/s on all eight drives. What if I connect a 24 port SAS expander to an eight port RAID controller, do I still get max throughput of 8 x 6 Gb/s, or am I able to get 24 x 6 Gb/s, assuming the expander is rated for 6 Gb/s on all ports?

Of course the PCIe bandwidth is going to limit it, as well as the RAID controller but is this right theoritically speaking? PCIe 2.0 x8 has bandwidth of 4000 MB/s and PCIe 3.0 x8 has 7880 MB/s.

As an example, I was thinking of buying LSI MegaRAID 9271-8i for my home server. It has eight internal SATA 6 Gb/s lanes. With that one I am able to connect eight hard drives and they can work on their limits in terms of transfer rates because there is one 6 Gb/s lane for each drive available. But in the future the storage capacity might be too low. I thought I could just add a SAS expander, like Intel RES2SV240. It is a 24 port expander rated for 6 Gb/s per port. So do I get the full potential out of the expander, to have 6 Gb/s connection for all the possible 24 drives? If so, could I buy the 9271-4i (has only four internal SATA ports) and the Intel SAS expander to be able to connect up to 24 hard drives and have them work at their full speed?

Yes and no...

Think about this: Your disks will not perform at 6Gbps (unless they're SSDs). So some level of oversubscription is okay when you go to using a SAS expander.

A more common scenario is the use of an external JBOD storage enclosure. Those usually have 1 or 2 x 4-lane SAS connectors linking them to the main server. Let's assume 4 x 6Gbps, so 24Gbps total bandwidth. Things are definitely oversubscribed there, as you may have 24 disks linked at 6Gbps... but recall that most disks won't be able to achieve more than 1.5 or 2Gbps in practice, so that level of oversubscription is okay.

Remember, 6Gbps is just a link speed. You will not be able to achieve that through an expander to all connected disks, because the expander has upstream connections to a RAID controller. The RAID controller is the limiting factor here.

See:
Do SAS expanders work transparently with SAS controllers?
How exactly does a SAS SFF-8087 breakout cable work? + RAID/connection questions

Real world experience (and a lot of money)... I built two machines each with (16) 512GB Samsung 850 Pros on Adaptec 81605Zs. Direct port connections with no expander. I got 6.2GB/s when the drives were fresh with WINSAT. Dropped to 5.8GB/s after a couple of days. Main problem is making sure motherboard slot was not shared with anything else. My personal machine has (8) SSDs via a LSI 9265-8i and the RES2SV240 expander mentioned above - 3.2GB/s. The other port on the apdater handles another expander with (13) drives - mechanical - nothing to write about. When the (8) SSD were split between a single port and sharing the second expander - performance was 2.7GB/s. Once again, bad or shared slot placement in a Rampage IV Extreme can drop these to 1.4GB/s. All RAID 0.