Men are allowed to marry up to 4 wives but its not an easy thing! and they have to fit the reason to marry more then 1.
as for Women marrying more then 1? first of all 1 man is enough headache. and no we can not marry more then 1.
Marrying cousins is allowed in Islam but not recommended!
Al-hamdu lillah (All praise be to Allah). There is no objection whatsoever in the Islamic religion for a man to marry any of his relatives except al-maharim (those forbidden for marriage) whom Allah mentioned in surat al-nisaa', 4:23 (interpretation of the meaning):
Prohibited to you (for marriage) are: your mothers, daughters, sisters; father's sisters, mother's sisters; brother's daughters, sister's daughters; foster-mothers (who breast-fed you), foster-sisters (who breast-fed from the same woman as you); your wives' mothers; your step-daughters under your guardianship, born of your wives with whom you have consummated marriage, no prohibition if ye have not consummated; (those who have been) wives of your sons proceeding from your loins; and two sisters in wedlock at one and the same time, except for what is past; for Allah is Oft-Forgiving, Most Merciful.