Skyrim allows one marriage and only one per Dragonborn, even if your spouse is killed - unless you use mods or console commands.

Others appear at random throughout the game. There’s a free one in a tent along the shoreline east of Dawnstar. It does not have to be an amulet purchased from Maramal, any amulet of Mara will do. You’ll also need to exhaust the dialog options with Maramal, the priest in the Temple of Mara in Riften, and be wearing an amulet of Mara in order to initiate a marriage proposal.

Housecarls will be wiling to wed you as soon as they enter your service, mercenaries must be hired first, and other candidates have fetch quests or other requirements.

You can marry anyone regardless of your Dragonborn’s race or gender, so long as you’ve fulfilled whatever conditions make them your friend. The Divines have blessed a total of 30 female marriage candidates and 37 male marriage candidates in The Elder Scrolls V: Skyrim and official expansions.