I was asked this open ended question in an interview once:
How would you find a solution to the normal equations with limited memory?
Unlike Solving sparse least squares system with limited memory, the matrix $A$ is not necessarily sparse. It could be dense.
The question was asked in a machine learning / stats context, so I gave the answer that instead of solving it exactly (e.g., with QR), you can solve it using stochastic or batch gradient descent and obtain an approximate solution.
In a linear algebra and scientific computing context, is there any way to solve a dense least squares system with limited memory?