IRA owners may have more than one Traditional IRA. If an individual signs one set of opening documents and makes contributions for subsequent tax years under that same plan agreement, only one Traditional IRA exists. If an individual has more than one IRA, she must aggregate all her contributions made to Traditional and Roth IRAs for a given year to stay within specified annual contribution limits. 

Example- If Sally has 2 Traditional IRAs, she can only contribute the maximum limit between both IRAs. 

IRA 1- $3,000

IRA 2- $3,500