Embraer 505 Captain reported performing a non-standard takeoff profile with excessive pitch attitude and bank angles which resulted in a flap overspeed during a non-revenue air taxi flight. The non-standard maneuver was completed and the flight continued to destination.

Narrative

Pilot in command (PIC) conducted a non-standard departure procedure; which led to a pitch attitude greater than 21 degrees and a roll attitude greater than 55 degrees for less than 90 seconds during takeoff rotation and the initial climb to an assigned heading and altitude. The non-standard event lasted less than three minutes in total; leading to normal recovered pitch and roll attitudes while conducting the level off on the assigned heading and altitude.While taxiing from the ramp for Runway XXR; the flight was initially cleared by ATC for runway heading and cleared to 2;000 feet altitude. PIC requested an unrestricted climb on course. ATC cleared the flight to 3;000 feet with a left climbing turn of approximately 90 degrees from runway heading. Normal before-takeoff checklists and briefings were completed as standard.Upon taking the runway; PIC set the takeoff power setting while holding brakes; verified takeoff power and engine parameters normal; conducted static takeoff; and at V1; rotated on schedule; and at positive rate; commanded gear up. At this time; PIC conducted a shallower than usual climb pitch attitude; during gear retraction; and at 400 feet of climb; commanded flaps up while accelerating. PIC then conducted increasing pitch attitude as flaps retraction was occurring; initially to 22 degrees; and reduced power while increasing pitch to 27 degrees of pitch; to compensate for increasing airspeed; attempting to avoid flap overspeed. During retraction; overspeed occurred for 10-12 seconds while retraction was completed. At approximately 1100-1200 feet on climbout; PIC initiated left turn to assigned heading at which roll attitude passed 30 degrees to approximately 52 degrees.Upon realizing that the maneuver was non-standard for profiles; PIC initiated recovery to normal flight perimeters of less than 30 degrees; and a standard pitch of 9-12 degrees was completed; with a level off on assigned heading and altitude without further incidence.The After Takeoff checklist was completed for the below 10;000 feet segment; and ATC cleared the flight onto a new heading and altitude to intercept the filed flight plan route. No discussion occurred between the flight crew of the nonstandard event; and the flight continued on to destination with no further issues or events after the initial level off for 3;000 feet before ATC further clearance on course.This event resulted in a pitch attitude greater than 18 degrees and a roll attitude greater than 30 degrees for less than 90 seconds during takeoff rotation and the initial climb to an assigned heading and altitude; and the total event lasted less than three minutes before normal pitch and roll attitudes were recovered while leveling off to the assigned heading and altitude. It also needs to be noted that No Revenue was on board this flight.Human factors: Distraction; Fatigue; Personal Issues; Physical Limitations; Poor CRM.Assigned initially on Day 0 to the Day 2 shift (XA:00 - XL:30). Then; on Day 3 into Day 4 (XA:11-XL:45) with a next duty assignment Day 4; the date of the event (XA:00-XM:15) into Day 5. It is worth noting that my last previous rotation for the company was the day shift; as well as is my time when I am on my off rotation.So; on this rotation; I was assigned to the Graveyard shift; and therefore; because I was not notified of this dramatic change in shift start time until the evening before my rotation started; I received very little notice to change and acclimate to the greater than 12-hour body clock change (Circadian Rhythm) conflict; which does not allow one to acclimate one's body to the requested/assigned operational assignment. Had I been given more notice of the new late shift assignment; I could have attempted to adjust to the dramatic change in pending duty time assignment; but I was not; so my body was in 'normal' duty time; along with the majority of the world to accomplish activities of daily life; such as medical appointments to obtain/maintain a FAA-mandated medical; personal family life; etc. This minimal warning of such a dramatic change in shift/body clock leads to sleep deprivation; adversely affecting the human body and its ability to get restorative rest so that one is able to perform safely and effectively.Also; when one is working the graveyard and alternative shifts; it is complicated to sleep during the day; especially in a hotel in the middle of the day due to sunlight streaming in; normal hotel noises like maids slamming doors; vacuuming; guests/maids talking in the hallways; and children running in the hallways; etc.Additionally; on the day of the incident; I was only operating on one meal before the flight because we checked into the hotel at XA:00; after duty/flying all night. Breakfast was unavailable at this early hour; so I immediately went to my hotel room; and despite the hotel noise and sunlight penetrating the hotel room; I attempted to sleep. As a result; we; as a crew; obtained our first and only meal of the day at XU:00; before coming on shift at XA:00. We had not eaten since the night before; and this does not truly meet one's nutritional needs.