The new issues pose additional challenges for Boeing’s leadership. Late last month, the company’s board fired chief executive Dennis A. Muilenburg. He is being replaced on an interim basis by Greg Smith, the former chief financial officer. Next week, David Calhoun, until recently the nonexecutive chairman of Boeing’s board, will take over as chief executive.

On an internal conference call last Thursday, the question of changing the wiring on the Max came up, according to the senior Boeing engineer and another person familiar with the matter. At one point, a Boeing employee asked about whether the fix would need to be made to every plane in the fleet if the issue was found to be low risk. Mr. Smith replied that if changes were needed, they would have to be comprehensive.

Mr. Smith’s sober response served as an immediate contrast to Mr. Muilenburg, who repeatedly made overly optimistic projections about what was needed to get the Max back into service.

Boeing was already confronting a number of problems with the 737 Max and its predecessor.

In recent simulator tests with crews from American, Southwest and United Airlines and Aeromexico, many pilots did not use the prescribed emergency procedures to handle problems with the flights, raising the possibility that regulators could mandate flight simulator training or change the procedures before clearing the plane to fly. The F.A.A. is evaluating Boeing’s analysis of the testing.

Still, there are signs that Boeing is making progress toward getting the Max flying again. Regulators from Europe plan to fly to Seattle this week to test the new software in a flight simulator, a sign that international authorities believe the company is far enough along that its fix is ready for serious evaluation, according to two people familiar with the matter.

Government officials believe that the plane may be cleared for a certification test flight as soon as this month, where the company must demonstrate the plane meets all the safety requirements. The flight — the regulator’s final exam for the Max — is a significant milestone and one of the last hurdles the company needs to clear for regulators to lift the grounding.

American Airlines and Southwest Airlines are currently planning to use the Max for commercial flights in April, while United Airlines has scheduled Max flights for June.