Hi,
This is pretty much how 99% of all synths work. Manufacturers don't put enough DSP power in them to allow you to have all sounds sound the same in multi-mode as they do in program mode. They do this mostly to keep the price down so people will actually buy them.
I use a Trinity Plus which is basically a keyboard version of the TR-Rack. You should be able to copy the program's fx to a particular multi-mode midi channel or part. The Master FX are also part of the program's sound so you'll have to copy these as well. However, the Master FX are shared across all multi parts so you'll want to have Master FX settings that will work with all parts that are sending signal to the Master FX busses.
You can also copy a combi into your Multi. When you do this, it can take up to 8 parts. A lot of multi's though only use 2, 3 or 4 parts.
There should be more info in the manual and you can probably try the Trinity Haven (
www.trinityhaven.com) for an faq.
HTH,
Fernando
p.s. - in case you're curious, about the only synths that I know of that don't lose their fx in multi-mode are the Nova and Supernova from Novation. These are 6 and 8 part multi-timbral and different beasts from the TR-Rack though (these are modelled analog synths or VA's).