Not having tried anything like that, I can only speculate as to what the results would be. I would say that the ST-2 is far more powerful than the antenna supplied with your receiver, so the likehood it would bolster the signal seems remote.

In addition, the use of a splitter typically reduces signal strength. Then you'd have two incoming signals going to a shared cable into the receiver. Collectively, that could very well reduce the efficacy of one or both antennas.

I suppose it wouldn't hurt to give it a try, but my gut tells me it is not an ideal solution. But if you do try the experiment, please report back your results.

One more thing...

I realize you're somewhat locked into the current location for the ST-2, but it may surprise you that even slight adjustments to the angle of the antenna can yield different results. It is a real PITA, but what I have done in the past is to grab a pair of walkie talkies and have someone sit in front of the receiver. I trek up to the roof, attic, etc. and tweak the location and/or angle of the antenna based on feedback from them.

You can try to go for a happy medium for all stations, or zero in on a favorite.