The query planner does not consider combining together clauses from different $or selectors in a cartesian product style, even when this would produce significantly more efficient index scans at the cost of having more individual index scans.

Steps to reproduce:

db.a.createIndex({ a: 1, b: 1, c: 1 });

let filter = {
  $and: [
    {
      $or: [
        {
          a: 0,
        },
        {
          a: 1,
        },
      ],
    },
    {
      $or: [
        {
          b: 0,
          c: { $gt: 0 },
        },
        { b: { $gt: 0 } },
      ],
    },
  ],
};

db.a.explain().find(filter).sort({ b: 1 });

This produces two index scans, both only constrained on the a field, merged using a SORT_MERGE.

A more efficient way would be to combine the two $or selectors using a cartesian product to produce four index scans, like the following query does with the same index:

let filter = {
  $or: [
    {
      a: 0,
      b: 0,
      c: { $gt: 0 },
    },
    {
      a: 1,
      b: 0,
      c: { $gt: 0 },
    },
    {
      a: 0,
      b: { $gt: 0 }
    },
    {
      a: 1,
      b: { $gt: 0 }
    },
  ],
};

db.a.explain().find(filter).sort({ b: 1 });

Note that the two queries are semantically equivalent, but all the index scans made by the latter are constrained on both the a and b fields, and two are additionally constrained on the c field, potentially scanning a significantly lower number of documents.