PORTLAND, Maine — Alexis Wright on Monday threw her legal support behind Mark Strong, the Thomaston businessman accused of helping her run a prostitution business out of a Kennebunk fitness studio, in Maine Supreme Judicial Court.

Wright’s attorney, Sarah Churchill, filed a brief Monday with the state’s highest court urging the panel to uphold the dismissal of 46 of the 59 charges against Strong.

The dismissal of the majority of the charges against Strong could set a positive precedent for Wright, who faces her own trial scheduled for May.

All 46 privacy invasion charges against Strong were thrown out by Justice Nancy Mills during a pretrial hearing Jan. 25, and Churchill has stated she plans to ask Mills to drop the same slate of privacy invasion charges facing her client as well.

The Superior Court-level decision to drop the 46 counts was immediately appealed by prosecutors to the state’s highest court. Monday at 4 p.m. was the Maine Supreme Judicial Court deadline for briefs to be filed by the York County district attorney’s office, as well as by additional interested parties such as Wright, in the appeal case.

In their initial brief, filed before the 4 p.m. deadline, prosecutors argued the dismissal of charges against Strong should not have been allowed in part because his attorneys did not file their motion to throw out the counts in a timely fashion. The York County district attorney’s office team argued in its filing that the Superior Court set a Dec. 6, 2012, deadline for all pretrial motions, yet Strong’s motion to drop the bulk of the charges came on Jan. 22.

The 46 disputed invasion of privacy charges are tied to the fact that the alleged sexual interactions between Wright and the johns were videotaped without the johns knowing.

Strong’s attorney, Daniel Lilley, argued that Maine privacy laws are meant to cover bathrooms, locker rooms and private homes, not to protect individuals engaged in illegal activity like prostitution. Prosecutors have countered that an individual committing a crime is not exempted from simultaneously being a victim of another crime.

Churchill, representing Wright, agreed with Lilley’s argument in her Monday brief.

“No individual can reasonably expect that they have a justifiable right to keep private criminal conduct they willingly participate in which occurs in a commercial setting or in the presence of third persons,” Churchill wrote, in part.

The trial of Strong, a Thomaston insurance broker and part-time private investigator, is continuing on in both York County Superior Court and the law court.

While Mills has refused to continue on with the trial until the supreme court rules whether the dismissal will be upheld, she has instructed attorneys to continue on with what she described in court as “housekeeping” work — such as finalizing evidence in the case — at the Superior Court level. That way, she said the trial will be positioned to begin in earnest on either the entire slate of 59 counts or the remaining 13, all of which are charges of promotion of prostitution, as soon as the high court decides on the 46 disputed ones.

The Monday afternoon high court deadlines are the first in a flurry.

By Tuesday, Justice Mills ordered Strong’s attorneys and those from the district attorney’s office to finish exchanging evidence in the case. Both parties have argued that they have not received all of their opposition’s evidence, becoming an early bone of contention in the trial.

By 4 p.m. Thursday, defense attorneys must file written reaction to the prosecutors’ Monday supreme court brief, and the district attorney’s office will get to file one more return salvo by Monday, Feb. 11. The high court will hear oral arguments in the case two days later, on Wednesday, Feb. 13.

Among the first items of business at the Superior Court level once the state supreme court rules on the disputed counts will be completion of jury selection, a process that ran in fits and starts in late January as attorneys struggled to find jurors who did not know anyone involved in the sprawling case or who were not influenced by the global media attention the scandal has attracted.