Will the stock holding period change from long term to short term when I add more shares into the stock?

You have two separate lots, both with 100 shares. One lot has been held for more than a year and thus will be taxed at the long-term rate. One lot has been held for less than a year and will be taxed at the short-term rate.

If you sell all your shares, you'd have long-term gains from the first lot and short-term gains from the second lot (or losses depending on how the stock has moved).

If you sold 100 shares, you'd have to determine what cost basis method you are using. There are three allowed methods-- FIFO, LIFO, and specific shares. If you are using FIFO, you'd sell the first 100 shares you purchased and realize long-term gains (or losses). If you are using LIFO, you'd sell the most recent 100 shares you purchased and realize short-term gains (or losses). If you use specific shares, you'd identify at the time of sale which of the two lots you were selling and could choose whether to realize short- or long-term gains. In general, using the specific shares method is the most tax efficient way to operate but it requires more record keeping than the other two approaches.