Multiple affiliate members on a site?

I want to join different affiliate sites do not want a separate page for each. Is it legal and possible to advertise and put links to different companies in one place? as if I was selling cosmetics for a company, used to sell cosmetics, then perhaps a different company for a different product? I suppose it as a sort of online mall, unless it is sold as a participant and not a trader Direct. If I pay my own site, would it not be possible to operate multiple affiliate programs from the site of my one? Or do not want other programs announced along with them? or, if not, and I'm new to this and just want as much information as possible before starting.

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