You generally can't have any "other coverage." The whole point of the combination of an HSA and HDHP is that if you have a high deductible plan (which policymakers like for various reasons, but leaves you with unpredictable expenses) you are allowed this powerful tax-free savings tool to save up for those unpredictable expenses. Getting supplementary coverage to make your expenses more predictable, defeats the purpose of the HDHP with HSA.
As noted, there are a few specific exceptions, see the linked instructions.
