Get more signal layers in Altium?
I suspect you want many many layers, so you can easily route. Typically people use VIAS to switch layers to jump over other traces.

Or you may want many many layers to keep traces well apart, to minimize crosstalk.

However, if signal fidelity is your goal, then using Ground Planes is the better approach.

A guy names Howard Johnson (had website) explained the crosstalk between traces will drop as 1/Distance^3, if the traces are OVER A PLANE.

Are planes a possibility?