As far as your question goes: no, if activating from .ini is not enough and you can't upgrade PHP, there's not much you can do. Some modules, but not all, can be added without recompilation (zypper install php5-soap, yum install php-soap). If it is not enough, try installing some PEAR class for interpreted SOAP support (NuSOAP, etc.).
In general, the double-dash --switches are designed to be used when recompiling PHP from scratch.
You would download the PHP source package (as a compressed .tgz tarball, say), expand it somewhere and then, e.g. under Linux, run the configure script
./configure --prefix ...
The configure command used by your PHP may be shown with phpinfo(). Repeating it identical should give you an exact copy of the PHP you now have installed. Adding --enable-soap will then enable SOAP in addition to everything else.
That said, if you aren't familiar with PHP recompilation, don't do it. It also requires several ancillary libraries that you might, or might not, have available - freetype, gd, libjpeg, XML, expat, and so on and so forth (it's not enough they are installed; they must be a developer version, i.e. with headers and so on; in most distributions, having libjpeg installed might not be enough, and you might need libjpeg-dev also).
I have to keep a separate virtual machine with everything installed for my recompilation purposes.