One way is to use grib_set with the key "scaleValuesBy". Let's say you have a field in orig.grib whose values you want to multiply by 2.1. First check the original data value statistics:
You could have also checked the statistics by "grib_ls -n statistics orig.grib".
Now let's scale all values up by a factor of 2.1:
And check the new values after the multiplication:
For adding or subtracting a constant, you can use the key "offsetValuesBy".