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Fan-based projects are usually tolerated, as long as there is no attempt to
profit without permission or utilize protected items in an in-appropriate
manner.  Satirical approaches offer a wider venue.

But it does not hurt to ask permission.  The worst that can happen is they
can say 'No!'  I would be very surprise if the subsequent set of rules
was not accept-able.

In the meantime, it doesn't hurt to discuss and speculate.  Once the
project has been worked up, an outline can be sent to the proper persons
for any necessary approval.

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The capture of the Doctor or Master could result in its owner needing to
buy it back with a particular token denoting a 'new life'.  The piece
must then be immediately place on the field on that turn, so that a player
must always maintain this particular piece on the field.

The 'new life' token can be earned during play.  It could start with one
player and shift between them as the goal pieces are ransomed.  So having
your Doctor/Master captured without a 'new life' token would mean the
loss of the game. This condition could be met as a simple checkmate, as a
player without a 'new life' token would not be able to leave their goal
piece under attack. 

I suggest that the Master player begin with this token, giving the Doctor
player the incentitive to make the first capture.