While editing the group use the Axes tool to set the group axis.
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On the subject of scaling, is there some reason SU doesnāt allow you to add or subtract X units in any particular direction like you can with the push/pull tool? In some cases I find I have to create guides where I want to end up and scale to it. Otherwise, I need to measure the current dimension I want scale, add or subtract the number of units I want to that number and type it into the field. Sometimes when Iām tired adding 3-19/32" to 5ā 11-5/8" to get my final dimension doesnāt just pop out of my brain. Just curious why the only options for the scale tool require me to know my final size, know my scale ratio, or snap to some existing point?
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You can try my extension s4u-Scale
https://extensions.sketchup.com/extension/b04497cd-fc6d-413e-a1ad-557365be19ca/s4u-scale-3
Thanks, I will!
Depending on the specific geometry modification desired, sometimes the Move tool can accomplish a similar effect and with exact relative adjustments. Select the geometry to be adjusted, trigger the Move tool by clicking-releasing somewhere, drag the mouse in the intended direction, then let go of the mouse and type in the exact desired change (e.g, ā3.375ā) and press Enter.
Thanks for the tip / reminder. I guess Iāve always known that, but it hasnāt come to mind in the moment. Maybe because I might be scaling a complex component, and exploding the nested groups in order select the geometry to move is something Iād rather avoid unless I have to. But Iāve been doing more rearranging of geometry with the move tool lately due to the easier inference locking and axis selection in the last update. Your suggestion fits right into that working style.
Why would you explode?
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How can I select geometry in different groups in order to move them together? When I open a group and make a selection, that selection doesnāt persist if I want to add selections from other groups. Iām probably unaware of some fundamental technique to do that. 
Natively you canāt move things in different groups together, but generally exploding things to manipulate them isnāt a good workflow.
There are a variety of extensions that will āStretchā multiple groups together. But it is important to use the appropriate tool for the job you want to do.
This is just one tool that springs to mind.
Thanks. I donāt like exploding groups either. Thatās a cool extension, but Iām not sure how often I need to do that. My original point was just wishing for the ability to add or subtract a fixed number of units using the scale tool. I thought I was missing something, but I guess the various workarounds are fine (setting guides, using move tool, etc.)