What has been a rapidly moving investigation securing damning testimony from witnesses who have defied White House orders may soon become a more arduous effort. Investigators are now trying to secure cooperation from higher-ranking advisers who can offer more direct accounts of Mr. Trump’s actions but are also more easily shielded from Congress…

At stake is not just how quickly the investigation concludes, but how much evidence ultimately undergirds the case against Mr. Trump.

Many Democrats involved in the inquiry already believe they have collected enough to impeach him for abusing his power by enlisting a foreign government to smear his political rivals. But to persuade the public — and the necessary number of Republican senators — that the president should be convicted and removed from office, they may need additional proof tying him directly to certain elements of the alleged wrongdoing. They could potentially unearth stronger evidence by turning to the courts, but that could also stall the case for months and risk losing public support, much as some Democrats believe happened in the Russia inquiry…

For now, Democrats have not yet exhausted testimony from officials who appear willing to cooperate and have at least peripheral knowledge of the case. At least two more White House officials are scheduled to testify this week, and are expected to confirm key events. Other officials from the State and Defense Departments involved in Ukraine policy are set to appear, as well.