The "Execute by name (Advanced)" option of the "Execute Another Command" action allows you to type in any command phrase, which will be resolved when the command executes.
If a command with that command phrase is accessible in any of the available profiles (I.E. within the active profile, a profile whose commands are included into the active profile, or a global profile), it will be executed.
Note "command phrase", E.G. if you have a command with the "When I say" contents "my command [with;] [option a;option b];my command with option c", you'd use something like "my command option a" in the "Execute by name (Advanced)" field (as if you were speaking the command), not the entire contents of the "When I say" field.
An alternative to multiple profiles would be to use variable keypresses, where you set text variables to the desired keypress (press F1 while VoiceAttack has focus to open VoiceAttackHelp.pdf in your default PDF viewer and see the "Quick Input, Variable Keypress and Hotkey Key Indicators" section for the syntax)
E.G. if you have a command that triggers off button 1, it could contain
Press variable key(s) [button1Action] and hold for 0,03 seconds and release
And you'd use a command like "using steering wheel a", containing something like
Set text [button1Action] to 'p' (save value to profile)
to change wheels (so that when you speak the command, button 1 is then set to press the "p" key)
Combined with a command that runs when your profile loads, to retrieve the last-used settings:
Set text [button1Action] to [Saved Value]
If you require more advanced commands mapped to buttons, rather than using a variable keypress actions in your button commands, you could use the "Execute Another Command" action with the "Execute by name (Advanced)" option set up something like
Execute command, '{TXT:button1action}' (by name)
and set the contents of "button1action" to a command phrase instead.