Maya: Trax Editor

In Maya open Trax Editor by going to Window -> Animation Editors -> Trax Editor.

Select all the joints (no IKs!) of a skeleton in Hypergraph or Outliner or in any method you like.

In Trax Editor go to Create -> Create Character Set.

Click on the stick figure icon to load the character set you just created.
Open Crete Clip Options window by select the square box next Create -> Animation Clip. Turn off Leave keys in timeline (an option for Keys), and select Put clip in Visor only as the option for Clip and Selected the option for Time Range. Make sure all the skeleton joints are still selected. Use shift-click to select all the keys for motion capture animation that you want in Timeline. Click on Apply in Create Clip Options window.

In Trax Editor, go to File -> Visor... In Visor window, select Character Clips tab. You should see one animation clip.

If you play back animation now, your character should stay still.

With middle mouse button pressed down, drag the animation clip from Visor onto the character track (which is the blue bar in the screen capture below) in Trax.

If you play back animation now, you should see your character playing the captured motion.

Drag the animation clip from Visor onto the character track in Trax again and put the two clips side by side. (See the screen capture below.)

If you play back animation now, your character should repeat the same motion twice. There is most likely a noticeable jump between the two clips.

Drag the second clip towards the first one so that the two clips overlap. A new track should show up below the first one. (See the screen capture below.)

With the Shift key down, select the two clips and click on the blend icon.
If you play back the animation now, the jump between two clips should be gone, although the transition may not look right.

For two motion clips to be blended seamlessly, in a certain number of frames of the clips the character must have similar spine shapes and have its weight on the same foot. Normally the shorter the duration of the clips used for blending, the better result you will get. So, you probably need to trim the clips by using Trim Before and Trim After to create better blending.

If your character slides in the blending, click the second clip with the right mouse button down, and select Attribute editor... from the pop-up window. Open Channel Offset tab, and select Relative for translate X, Y, and Z of the root joint.

You can blend any number of motion clips and also split, merge, trim, cut, copy, and paste motions in Trax.

Sample animation file