The layered approach is standard practice among experienced travelers: let the home or domestic policy be the base, then buy targeted cover for the gaps rather than paying twice for the same protection. The usual gaps are predictable. Domestic health plans that partially cover foreign emergencies almost never include medical evacuation, so a travel policy with strong evacuation and repatriation cover is the most important supplement. High out-of-country deductibles or low reimbursement percentages can be offset by a travel medical policy that pays from the first unit of cost.
A useful detail: some travel insurers sell cheaper secondary coverage that pays after your primary insurance, versus primary coverage that pays first regardless. If your home plan genuinely covers a lot abroad, secondary cover can be economical; if it covers little, primary is simpler when claiming.
Similarly, home contents insurance sometimes covers belongings abroad, letting you skip baggage cover, and a card may handle trip cancellation. Map what you have, list what's missing, and buy exactly that.