Step-by-step guide

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:

% grib_ls -p min,max,avg orig.grib
min         max         avg
234.554     312.085     278.977

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:

% grib_set -s scaleValuesBy=2.1  orig.grib  out.grib

And check the new values after the multiplication:

% grib_ls -p min,max,avg out.grib
min         max         avg
492.563     655.376     585.853

For adding or subtracting a constant, you can use the key "offsetValuesBy".