The simplest way to offset an animation is to sandwich in a new parent:
Here, I started with an object with a single location keyframe, animated by an f-curve modifier. Then I duplicated the object and parented it to an empty. Finally, I moved that empty to create the offset that I wanted.
This can be done for location, rotation, or scale offsets.
If the object is already parented to an object, you should sandwich in the new parent: parent the object to the empty, then parent the empty to the original parent of the object.
This doesn't require any kind of fiddliness or math, and can be done to eye as easily as numerically, just by controlling the new parent's transform. There are similar techniques involving delta transforms, but deltas are a weird, out-of-date, not-quite-there solution to the problem, and so I avoid deltas whenever possible.