Does it sound reasonable to do the Hatch program 2 days a week at home and lift with the local club once a week for heavy singles for both lifts once a week?
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"Do or do not...there is no try."
That shouldn't be a problem. On the heavy single days your total volume will be significantly lower than your squat days. Especially if you have a rest day day in between the squat and heavy single days. You could even throw in a technique day where you use lighter weights and focus on speed and massaging out some technical glitches you may have. Ultimately you need to monitor how your feel during the workouts and your recovery between. If you are recovering properly you should not have any major issues. You never know unless you try. Record your efforts and adjust as needed.
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