Changing the lunar day does not guarantee a different main-star layout. The traditional Zi Wei calculation can map different days to the same position within a bureau.
A calculation example
Under the common remainder method for Water Two Bureau, day one is increased to two. The quotient is one; counting from Yin and retreating one position places Zi Wei at Chou. Day twenty-five is increased to twenty-six. Its quotient of thirteen returns to Yin around the twelve positions, and the same retreat again reaches Chou.
This demonstrates a repeated result, not a rule that every adjacent pair of days matches. Each proposed date must be calculated.
Other stars can still change
Day-dependent auxiliary stars may differ even when all fourteen main stars remain in place. Check those as well as the displayed birth date.
The example holds other inputs constant. Crossing a lunar month or year boundary introduces additional changes. Matching one layer cannot establish identical lives or settle an uncertain birth date.