There is no code prohibition to splice wire onto the feeders that currently hook to the main lugs, despite what some may tell you. Yes it will look goofy, but it will get the job done without having to add a subpanel. Google Polaris lugs.
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As one who is regularly involved in doing load calcs for residences, it is amazing how much load a 200A panel will take. 3500 Sq ft house with 3 ac units and a detached garage shop and a pool usually comes in under 175A in the overheated sunny desert I live in. If you have open slots in your...