Sort a Map first on Object.property1 and then for each Object.property1, sort by Object.property2?

You only need one comparator. First compare the taxids. If they are unequal return -1 or 1 as appropriate.

If they are equals, then compare the provider name.

Your null-handling violates the contract of compare, as you deem null equal to any other value, while the JavaDoc writes.

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