There is a basic misconception in the question you have asked, which @biogirl has explained. There is only one start Codon in any mRNA and it defines the open reading frame.
All other AUGs in the open reading frame are simply codons that encode for the Amino Acid Methionine and have no function in the start of translation. There are factors other than AUG that determine the start of translation.
So a frame shift that gives you an additional AUG only means that you will have a different Amino Acid encoded for in the resulting polypeptide. A frame shift will generally completely alter the protein product of the gene. If however the frameshift does disrupt the start codon, then it is unlikely that you will have any translation what-so-ever, as the other elements necessary for determining the start of translation will likely not be present in other areas of the coding sequence. In prokaryotes, you need a Shine-Delgarno sequence to initiate translation, and in Eukaryotes, though all of the factors for translation start are not well understood many genes carry a Kozak sequence that indicates to the ribosome the start of the open reading frame.
The more important codons to look for are introductions of stop codons. These three codons, UAA, UAG, and UGA do not have tRNAs with complementary anticodons (for the most part, as tRNA genes can also sustain mutations that change their anticodon) and therefore all result in the termination of translation if the shifted frame results in the ribosome reading one of the three stop codons in frame.