Hello Esther and welcome back!
The short answer to your question is that the same mechanisms utilized by cells to regulate transcription before cells have replicated their DNA and are 2n (discussed in our previous answer) are utilized after cells have replicated their DNA and are 4n. Of course, certain transcription factors and other regulatory proteins may be specifically expressed during the G2 stage of the cell cycle, but the mechanisms are not unique – nor do they need to be.
Keep in mind that even a cell that has 2 copies (instead of 4 copies) of a given allele must precisely regulate transcription and constantly maintain the appropriate levels of transcription. You are right to assume that an increase in “gene dosage” could be catastrophic to a cell, remember that G2 is a transient stage and that all of the genes in the cell are “in excess” because the entire genome is replicated during S phase. To the best of our knowledge, the two alleles of a given gene that are present on each sister chromatid will be transcribed at similar levels during G2.
Furthermore, during the early stages of mitosis, the DNA strands (or chromatin) become more and more condensed making it physically impossible for the transcriptional machinery to gain access to much of the DNA so that transcription essentially stops. Therefore, the majority of the genes carried on these compacted chromosomes, or chromatids, are not transcribed (even in the absence of any additional regulatory mechanisms).
We hope this helps clarify your view of this fascinating process! Please let us know if you have further questions.