Tim very nicely illustrated an aspect of training that new students struggle with to understand.
Kaeshi Waza (reversal of technique) was also mentioned as a training aid which adds to the chess aspect you want to experience.
Henka Waza also enters that area of training where you find the chess aspects. For Nage that will probably give you more chess play than Kaeshi waza since Henka Waza is practice for the person applying a technique to feel what is happening with his uke and if ukes attack changes as a reaction to the applied technique or his body goes somewhere not intended then you change your 1st technique to something else more appropriate rather to try and force your original technique.
One other practice that may fit is Renraku?Renzaku? (not sure which is proper) waza which is linking techniques together each one properly applied but done as a series of techniques that flow together all the time keeping control of uke.
You may not get to see these or practice for a while as I haven't seen them much except as advanced training.
I have heard some instructors actually say not to practice them to much but rather focus on perfect application of your 1st technique so follow up techniques won't be needed.
They are fun though and I think get into the chess part you are thinking of.