Yes, you can run multiple sound cards in a PC.
There is a limitation:
If both cards are the same, the drivers have to support multiple cards. Sound Blaster brand of cards, for example, don't.
What's that Phillips card, is it the 5.1 ?? Check the chip labeling on the card and compare it to your SB 5.1. I'm thinking that the Phillips could really be a SB 5.1 (based on the EMU chip) but I don't really know for sure. There's not alot of info around on the Phillips card since the distibutor is out of biz and those things are being liquidated cheap, with little to no support. You'll have to check that out. If it's really a rebadged SB, depending on the drivers, it might work, but probably not. If it's a different chip on the Phillips then on the SB 5.1 then it should work just fine.
From the sounds of it you are doing DAW on your system. There's a small chance you might have to move things around slightly to prevent dropouts or on either card. Load up 4 tracks and crank 'er up. If the sound studders or drops out on any track, try one of the cards in another slot. Get them both as far away from the video card and recheck it.
It might take a little tweaking, but it's usually pretty easy. I've even seen setups with 4 sound cards in them !!
Good luck,
Dukey