Here is a diagram that illustrates how such an installation might look.
Iron filter before or after water softener.
As a softener also backwashes any debris and sediment making its way through will be flushed away during backwash while at the same time expanding the space between the resin beads to increase brine contact.
Should you place it before the pressure tank then the filter will not automatically backwash.
Why you may want a post filter after your water softener.
Since softeners are not designed to address undissolved iron and manganese a whole house particle filter is good solution for reducing and or eliminating insoluble iron and manganese.
Each filter will need a particular pressure and flow rate to function optimally.
The neutralizer should be installed before your iron filter and water softener.
Why you might need a sediment pre filter before your water softener.
Most iron filter medias will typically oxidize the clear iron and then filter out the solid particles which are then flushed to drain during the backwash cycle.
Although most water filter cartridges that are used as a pre filter are not fine enough to capture non dissolved iron in the water a 5 micron pre filter cartridge is fine enough to capture iron particles.
Again this particle filter can also serve as a barrier protecting your water softener conditioner from clogging and thus extending the life of your unit.
Note that this installation includes a pre filter before the neutralizer.