It's very simple to do this by using Animation Layers. Put different objects into different layer and you can control which to continue with its own animation & which object is going to freeze during the playback.
If you have set the animation prior to assign an animation layer, it's very easy to accomplish this, simply copy the Base Layer and Paste in New Layer. However, bear in mind that copy & paste the animation layer of Container doesn't clone the keyframe from the base layer to the new one. This is rather annoying but I couldn't find any immediate solution right now.
There is a key transfer script on www.scriptspot.com but someone claimed that it doesn't work well with 3dsmax 2012.
Hopefully we got better option in 3dsmax 2013, although I know this is barely possible. Haha~