Call with user and password: Is it possible to use a call statement like this:
call "BAPI_..."  user="ANOTHER_RFC_USER"  ....

Yes, this is possible, but in this case you need to specify the full RFC connection string, including user and password. Use the "RfcConnect" statement

RfcConnect parameters="...."

where you specify the RFC connection parameters in SAP notation, e.g.

RfcConnect parameters "USER=xxx PASSWD=yyy CLIENT=000 LANG=E ASHOST=zzz SYSNR=2"

Then perform a normal Call statement and finally reset the RFC connection parameters with

RfcConnect parameters=""