I would say, for the most part, that the command of a girl's owner would supersede the command of another.
However, there is at least one example I recall where this is not the case:
"You are quite alone, Lady Elicia," he said. "There are none to hear your screams."
He was tall and strong, clad in a warrior's scarlet. At his belt there was a long leash, looped.
"Emerge from your bath," said he, "and prepare to accept slave bonds."
"No!" she cried. Then she cried out to me, "Run, Judy! Fetch help!"
"Do not," said the man.
"Yes, Master," I said. I looked at the Lady Elicia. "Forgive me, Mistress," I said. "I am a slave girl who has been commanded by a man." I knelt to one side.
Slave Girl of Gor Book 11 Page 392
And then there are these quotes, which don't quite speak to your question, but do show that others may get involved in the behavior of a girl owned by someone else.
"Any Free Man may discipline an insolent or errant slave," I said, "even one who is the least bit displeasing, even one he might merely feel like disciplining. If she is killed, or injured, he need only pay compensation to her Master, and that only if the Master can be located within a specific amount of time and requests such compensation." In virtue of such customs and statutes the perfect discipline under which Gorean slaves are kept is maintained and guaranteed even when they are not within the direct purview of their Masters or their appointed agents.
Players of Gor Book 20 Page 235
"You cannot punish me!" she cried. "You are not my Masters!"
"Any Free Person can punish an errant slave girl," I said. "Surely you do not think that her behavior fails to be subject to supervision and correction as soon as she is out of her Master's sight?"
Magician of Gor Book 25 Page 225
The discipline of a slave may be attended to by any Free Person, otherwise she might do much what she wished, provided only her Master did not learn of it. The legal principle is clear, and has been upheld in several courts, in several cities, including Ar.
Magician of Gor Book 25 Page 122
"You are not my master," she said. "You cannot whip me!"
"Are you sure of that?" I asked.
"No," she said. She then looked at me uncertainly. Perhaps for the first time she sensed she was looking into the eyes of a man who could bring the whip to her back and legs. I saw she was trying to deal with this thought. Too, I saw a flicker in her eyes, perhaps of fear, but, too, perhaps of something else, as well.
She had never before been, I suspected, subject to a male.
Swordsmen of Gor Book 29 Page 60
"Do you not object to the fellow switching Nezumi?" I asked.
"No," said Tajima. "It will be good for her, and we must remember that we are guests here."
"We would not wish to be discourteous," I said.
Rebels of Gor Book 33 Page 320