Is it possible to move an object closer or farther away while keeping the same perspective? If I grab an object and move it left or right, or up-and-down, it moves in a path perpendicular to my current view. Is it possible to move an object parallel to my current view?

In other words, I want the object to move closer or farther away while maintaining the same relative position in my view. 

Is this capability built into to blender?
If I got what you ask yes, it's possible, switch to view transform orientation then grab the object and press ZZ (constrain the grab on view Z axis):