You can get both, but your SSI is likely to be reduced by the amount of alimony over twenty dollars monthly that you recieve, which could reduce it to zero.
if your on SSI you can also draw alimony long as you don;t draw more than you are allow. because while your on ssi your only allow to make what they allow you too
Social Security Income is based on income and alimony is considered an income. The cap is about $2200 a month. If total income is less than that you can apply.