Sprint Corp on Tuesday unveiled a new option called “framily” plans that give up to 10 family members or friends big service discounts if they sign up as a group, the latest move in an increasingly competitive market. The new option, which could represent a service discount of almost 50 percent from Sprint’s existing family plan in some cases, follows aggressive discounts by Sprint’s smaller rival T-Mobile US that sparked a new wave of competition. T-Mobile’s chief executive officer put the spotlight on family plans last week when he said winning over rivals’ family plan users was a New Year’s resolution. T-Mobile is seen as an acquisition target by Sprint, which is 80 percent-owned by SoftBank Corp. Operators have long offered discounts through family plans because they help to retain customers as it is harder for groups to switch than for individual customers. Sprint is taking the concept a step further by letting friends and neighbors join “framily” plans and providing them with separate bills.