Shift register that can source +-15V?
As I see it you have three requirements:


You want to convert a 0V to 5V TTL signal to -15V to +15V - which you can supply;
You have a large number (>20) of outputs that you want to control with a minimum of TTL-level microcontroller pins;
You only need one output to be at +15V at once.


That last implies that you want a 5-to-32 demultiplexor, not a shift register - although a shift register would need only 3 pins, at the sacrifice of speed to change the outputs while the new "ON" pin was shifted into place:

a. Clock;
b. Shift-in data;
c. Latch output.

Regardless of the format though, you have a 0/5V signal that you want converted to -15/+15V. That basically precludes a lot of semiconductor solutions such as FETs and transistors, since their outputs are based on their inputs (including triggers); and you want more than that.

You mention serial converters: there are two versions of these. One that uses an input to switch the +/- supply (à la the 1488, but that's limited to 10mA max output); or a charge-pump device such as the MAX232 which makes its own +/- voltage from the 0/5V supply. The former is not strong enough; the latter is unnecessary (you have the voltages, you don't need to create them) and expensive - and probably also not strong enough.

So you could control a bank of relays, either solid state or mechanical, or a bank of high-current op-amps. For the op-amp solution, something like TI's LM7332 dual op-amp may work:


It can be supplied with +/- 15V;
It offers 100 mA on its outputs;
You can supply the desired 0-5V signal on the non-inverting input;
Put a reference 2.5V from a voltage divider on the inverting input.


If the non-inverting input is below 2.5V, the op-amp will drop to the negative voltage. Above 2.5V, the op-amp will jump to the positive voltage.