The speech domain prevails in the spotlight for several natural language processing (NLP) tasks while the singing domain remains less explored. The culmination of NLP is the speech-to-speech translation (S2ST) task, referring to translation and synthesis of human speech. A disparity between S2ST and the possible adaptation to the singing domain, which we describe as singing-voice to singing-voice translation (SV2SVT), is becoming prominent as the former is progressing ever faster, while the latter is at a standstill. Singing-voice synthesis systems are overcoming the barrier of multi-lingual synthesis, despite limited attention has been paid to multi-lingual songwriting and song translation. This paper endeavors to determine what is required for successful SV2SVT and proposes PolySinger (Polyglot Singer): the first system for SV2SVT, performing lyrics translation from English to Japanese. A cascaded approach is proposed to establish a framework with a high degree of control which can potentially diminish the disparity between SV2SVT and S2ST. The performance of PolySinger is evaluated by a mean opinion score test with native Japanese speakers. Results and in-depth discussions with test subjects suggest a solid foundation for SV2SVT, but several shortcomings must be overcome, which are discussed for the future of SV2SVT.