Ok, I think I understand.
The 3 groups of 10 shift registers, each with its own SS line (the lines connected to 3 Arduino pins) would fix the signal problem for the SS line because each Arduino pin would only be connected to 10 inputs. But the problem would still remain for the Arduino CLK pin which would be connected to 30 inputs. That line would need buffering. BTW, this problem is known as a "fan out" problem because the lines looks like a fan when drawn on a schematic.
If you use 3 Arduino pins as CLK pins, you would fix that problem too. Each would have a fan out of 10. But then you could not use the hardware SPI. You would need to use the shiftOut() function, which is much slower. This may not be a problem for your project, depending what speed is required and what else the Arduino is doing.
As Mike said, the MOSI/DATA line is not a problem. It would only be connected to 3 inputs, the first of each group of SRs. That is only a fan out of 3, so no problem. And for the other 9 SRs in the group, the signal is buffered by the previous SR, so that's ok too.