You can choose whoever you like to be your birth partner, though the doctors and nurses might object if you have a team of people! If you do want more than one partner, get approval ahead of the birth and put this in your birth plan (see Your birth plan and Birth ideologies). You may want to ask your mom, sister, or close friend in addition to your partner. You might also find that your partner is unable to be there, for example if he is unavoidably going to be out of the country. If you're comfortable with it and feel that you will benefit from someone else being there, then ask away. You can put who you want to be your birth partner or partners on your birth plan. Of course, if you're going to ask someone else other than, or in addition to, your partner to be present, discuss it with him first. He might not be so thrilled at the idea of your mom being present, but explain why you would like her there. Remember that this is a special occasion for him as well and he may have his own preferences for who is or is not present at the birth.
Now might also be a good time to discuss things like whether you want a video made of the birth, but you may prefer that your partner supports you, rather than handling the camera!