Question: “Can you work on a ladder that is above the height required for fall protection? If yes, can you use two hands to work. If not, can you point to the specific regulation that prohibits this? Thanks!”

Answer: Yes, yes, and there is no specific regulation addressing either circumstance. General guidance is to “…always maintain a 3-point (two hands and a foot, or two feet and a hand) contact on the ladder when climbing.”

Recent rule-making for 1910.21 - 1910.30—Walking Working Surfaces—aligned existing General Industry regs more closely with OSHA’s construction standard, but says nothing about the hands free approach when performing work atop a ladder:

1926.1053(b)(21)

Each employee shall use at least one hand to grasp the ladder when progressing up and/or down the ladder.

1926.1053(b)(22)

An employee shall not carry any object or load that could cause the employee to lose balance and fall.

Ladders –1910.23: GENERAL REQUIREMENTS:

• Ensure each ladder used meets requirements of section
• Covers all ladders except when ladder is used in emergency ops, designed into or “integral part” of machines/equipment
• Ensure ladder and stepstool rungs, steps, cleats meet spacing specs in rule
• Ensure wooden ladders are not coated with material that could obscure structural defects, and that metal ladders are protected against corrosion
• Ladder surfaces must be free of puncture and laceration hazards
• Ladders must be used only for the purpose for which designed
• Ladders must be inspected BEFORE initial use in EACH work shift, and more frequently as needed, to identify any visible defects that could cause injury
• Ladders with structural or other defects must be IMMEDIATELY tagged “Dangerous: Do Not Use” or with similar language and removed from service until repaired or replaced
• EEs must face ladder when climbing up/down
• EEs must use at least one hand while climbing, and cannot carry objects/loads that could cause the EE to lose balance and fall while climbing

This OSHA Quick Card is instructive for best practices, but doesn’t cite anything.

And this letter of interpretation helps make clear the question…

Portable ladders: fall protection is not required for employees climbing or working on portable ladders.
Neither the ladder standard (29 CFR 1926, subpart X) nor the fall protection standard (29 CFR 1926, subpart M) requires fall protection for workers while working on portable ladders.

You note that a number of general contractors in Georgia "are attempting to require personal fall arrest systems for their subcontractors working on ladders 6 feet or higher." Although the OSHA standards do not require fall protection for workers on fixed ladders below 24 feet or on portable ladders, we encourage employers to provide additional protection.

Learn more about OSHA construction standards.

Source? https://www.osha.gov/pls/oshaweb/owadisp.show_document?p_table=INTERPRETATIONS&p_id=23870