Amplification of magnetic field can we by any means amplify magnetic signal as we can with electric signal. As both electric and magnetic field can be represented in the form of a wave the analogy seems to be natural. 
I want the input and output as magnetic signal. 
 A: There are several ways to amplify the magnetic field, though the mechanism is not same as for electrical signal amplification, but still they are fruitful. 
compression:- since a magnetic flux through a surface remains conserved, if we compress the field lines or stretch (or fold) the field line then we can increase the energy by working against the field force. in this process even the field topology will remain invariant. By linear winding of field lines we can create a toroidal field.
another important way is amplification of Alfven wave.
A: I presume your idea revolves around permanent magnets, if so stacking decreasing sized magnets in a pyramid configuration grants you a powerful localized field at the smallest point. Halbach configurations allow for combined field manipulation which comes with the downside of slowly degrading the total field strength over time. 
Please do let me know what you find as I am researching a similer querry.
A: Electrical amplification is about using an input signal to modulate a larger amount of power that comes from a separate power supply of some sort.
And yes, there is such a thing as a magnetic amplifier that works on a very similar principle (even though the inputs and outputs are usually electrical). But you can't get an output value that's greater than the sum of the input values (control signal plus power source).
