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(CNN) —  

While special counsel Robert Mueller technically had a new boss at the Justice Department as of Wednesday afternoon, the day-to-day work of the probe forged ahead on Thursday.

Deputy Attorney General Rod Rosenstein’s top deputy, Principal Associate Deputy Attorney General Ed O’Callaghan, met with lawyers from the special counsel’s team, according to a source familiar with the matter – just as he has been doing on nearly a biweekly basis for months, as CNN previously reported.

It’s a small but illustrative example of how the Mueller probe is likely to function, at least for the time being, in the wake of the abrupt ouster of Attorney General Jeff Sessions.

For nearly 18 months, Rosenstein has overseen the special counsel’s investigation into Russia’s interference in the 2016 election because Sessions had stepped aside from all matters related to the presidential campaign.

But when Sessions’ chief of staff, Matthew Whitaker, leapfrogged over Rosenstein and was named acting attorney general in his boss’ place Wednesday afternoon, questions immediately began to swirl about who Mueller would report to, whether Whitaker must recuse himself from the investigation given his fierce criticism of it, if Rosenstein would quit and whether Mueller’s work will be curtailed.

Whitaker has given no indication he believes he needs to step aside from ultimately overseeing Mueller’s investigation, one person familiar with his thinking told CNN Thursday.

That belief is echoed by White House officials who also do not believe Whitaker needs to recuse himself, sources tell CNN.

From a practical standpoint, one of the sources said, it would defeat the entire purpose of naming him as acting attorney general since Trump railed against Sessions for recusing himself from the Russia investigation.

But Rosenstein is expected to continue to handle the day-to-day management of the probe, as he would for any other significant criminal investigation.

One source described it as “business as usual.”

However, the arrangement may prove challenging down the line, or quickly, if Whitaker and Rosenstein disagree on any significant matter.

As the Washington Post reported Thursday, people close to Whitaker do not believe he would approve Mueller seeking a subpoena of President Donald Trump.

While Whitaker has made questionable comments that could create the appearance of a conflict of interest, there isn’t an explicit conflict under Justice Department rules, as might arise if – for example – he had a family member under active investigation.

According to department procedures, Whitaker would have to initiate an ethics review about a potential problem and has not yet done so. And even if ethics advisers at the Justice Department suggested he step aside, Whitaker is not obligated to follow that advice, sources explained.

One senior White House official noted that the Sessions situation was different. As a campaign surrogate, Sessions was arguably “substantially involved in the conduct that is the subject of the investigation,” according to Justice Department regulations. Whitaker’s writings do not fall under that requirement in the White House’s view, though by Thursday evening senior officials were growing uneas