The possibility to change SPI setup in software depends on the SPI core you are using.
IIRC the standard SPI core available in Qsys doesn't allow this, but other 3rd party cores do. In such cases it's a matter or writing proper values in the control registers.
The main problem can be with the slaves which would decode in the wrong way spi data and you could mess up everything. Probably you can manage this with slave select lines,
provided that your slave doesn't complain about 'abnormal' spi traffic when its SS is deasserted.