Depends on what kind of car you are building. Cutting the core support can be a good idea on a race car since then you can pull the engine and transmission straight out the front. The core support typically isn't cut on a street car though. On my '72 Duster I had the stock core support cut out and replaced with the US Car Tool core support so I could use a full size radiator. It is a lot of work but it sure solves a bunch of problems.
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