Hello,
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If the composition of both the birth control pills are the same, then you will have same protection continued. If the hormonal composition of the pills are different, then there will be changes in the regular hormonal level. You might have alterations in your bleeding pattern.
I would suggest not to mix them. Be more careful with regular pill intake and follow the norm for the missed pills if you miss any pill in between.
For more detailed discussion, visit your gynecologist, and ask for alternative birth control that is easy to maintain like IUD, patch or implant.
Hope this helps. Take care.