(CNN) -- Ex-New England Patriot Aaron Hernandez has two separate scheduled court appearances this week, taking on his former team and challenging a search warrant in the murder investigation of Odin Lloyd.
On Monday, a judge may firm up a trial date in Lloyd's death, now penciled in for October. Hernandez has pleaded not guilty both in the June 2013 shooting of Lloyd, and in a separate Boston case, the drive-by double slaying of Safiro Furtado and Daniel Abreu. That trial is already set for May 2015.
While he waits for trial, Hernandez wants to move to a new jail.
Since his arrest in June 2013, Hernandez has been held at the Bristol House of Corrections in a 10-feet-by-7-feet cell.
His legal team is asking a judge to transfer him closer to their Boston offices to make their commute shorter. A judge is expected to rule on that request Monday.
In court documents, prosecutors aren't objecting to the move, but they are objecting to other defense accusations that the Bristol sheriff who runs the jail has "collaborated... in an effort to generate evidence to be used against Hernandez."
The defense also complains that they are assigned to a specific visitation room and unable to have private conversations with Hernandez.
Sheriff Thomas Hodgson and prosecutors deny they've done anything wrong.
On Wednesday, in a second court appearance this week, Hernandez's defense team hopes to get a court-approved subpoena to demand the New England Patriots turn over all medical records and psychological tests involving their former star tight end.
A motion calls the records potential evidence that may bear upon Hernandez's state of mind and "physical and mental state" prior to Lloyd's murder.
The move indicates his attorneys might be considering a diminished capacity defense -- being less capable of knowing right from wrong -- legal experts said, if there is credible evidence.
"My instinct is they try to argue he wasn't mentally capable of planning or intending any murder, and thus, first degree murder should be off the table," University of New Hampshire law professor Michael McCann told CNN.
Hernandez also is waiting for a ruling on another defense motion to throw out the murder charge, arguing the state has failed to meet minimum standards called probable cause to make that charge stick.
In a June hearing, his lawyer Jamie Sultan told a judge all he's heard is "a lot of smoke" but few specifics.
"Who killed Mr. Lloyd? Why? Whether it was part of a plan and if so, whose plan? What happened to the car, and what happened at the scene?" Sultan argued in that hearing.
The defense is also trying to quash a June 18, 2013, search warrant executed at Hernandez' home. Along with cellphones, an iPad and other items, the search turned up evidence including surveillance video from interior cameras.
The images include a still allegedly taken shortly after Lloyd's slaying that shows Hernandez holding what prosecutors believe is the murder weapon, according to a law enforcement source. A .45-caliber gun allegedly used to fire eight shots has never been found.
Defense attorneys argue investigators did not have the legally required search warrant paperwork with them.
In a motion, Hernandez' lawyers state a Massachusetts state trooper entering the house "clearly has no file folder in his hand," with documents.
If the defense successfully quashes the search warrant, the pictures from that search could become inadmissible.
Prosecutors maintain the search was carried out by the book.
CNN's Michelle Rozsa and Laura Dolan contributed to this report.
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