Is there an "additive manufacturing" method to make an ASIC?
Having a protoype ASIC manufactured is not very expensive when older technologies from 130nm up are used. The software tools needed are usually much more expensive since the market is quite small. From this point of view it does not make much sense to work on that problem.

It is possible to produce wafers and put them "on hold" at a certain stage during production. Doing this before the final layers of metal interconnect are made it is possible to continue production at a later point in time and produce a few variants of a chip. As a final resort focused ion beams can be used to remove and add tracks but this a very slow and expensive process.

A more interesting approach could be organic electronics where basically an ink-jet printer is used to generate electronic devices.