That depends on what you mean when you say "multiple speakers".
That card has four jacks on the back for 3.5 mm stereo plugs. One (the pink one) is for input from a microphone; the three others are for speakers. The card is designed for use in a 5.1 speaker surround sound system. What that means is that three jacks are outputs for specific speakers:
(a) the GREEN one is for the two front speakers, left and right;
(b) the BLACK one is for the two rear speakers, left and right;
(c) the ORANGE one is for the front cnter speaker and the front subwoofer.
Of course, the card also has an internal connector to feed some signals to your computer's front panel headphone / microphone jacks.
So if that's what you want - a 5.1 surround sound system with those 6 speakers - the card can be used exactly as designed.
If you plan to use fewer speakers - for example, a 2.1 system (front left and right, plus subwoofer) you can do that also. All the options are covered in Section 5 of your manual.
Now look at your manual's Section 6.2.2 on p. 24. It shows you how to change the card's output mode to match the speakers (and / or headphones) you have connected. To get to these settings, see p. 21 of the manual - it's done via an icon in the system tray. Check how this is set. By default it may be set to front speakers only (a 2.1 system) or headphones, which means it will not send out anything to other speakers. Set it to your real speaker setup.
That's how the card is designed. However, if your plan is to have several sets of speakers that are only front speakers (left / right and maybe subwoofer), the card itself won't do that. You will need some way of splitting the signal being fed out of the card to extra speakers, or you may do it by feeding the card's output to a separate amplifier that does provide multiple speakers outputs.