EPSG:9806 is the transformation method called Cassini-Soldner, but this is not the kind of EPSG code that includes the transformation parameters which are necessary for QGIS.
Usually, shapefile datasets include a .prj file with the CRS information. If you do not have it, you might go back to the place where you got the data from and look for further information.
Filtering the QGIS CRS list for Monte Mario, you get a bunch of 7 transverse mercator projections covering parts of Italy. The main CRS are based on the 9° (EPSG:3003 zone 1) and 15° (EPSG:3004 zone 2) meridian. CRS with prime meridian through Rome and the region Emilia Romagna have separate CRS definitions.
You need the center coordinates of the 31 local Cassini Soldner projections, which you can find here: http://www.globogis.it/le-origini-delle-coordinate-cassini-soldner
Note that the given Eastings are not based on the Greenwich meridian, but on local datums used, which you can find here: http://www.globogis.it/i-datum-catastali-italiani
You will have to add datum and center eastings, and transform the degree-minute-second values into decimal degrees for lat and lon.
With that, you can build your local CRS:
+proj=cass +lon_0=.... +lat_0=.... +x_0=0 +y_0=0 +ellps=bessel +units=m +no_defs
You might have to add a datum shift to switch from the bessel ellipsoid to WGS84.