May one answer Baruch Uvaruch Shemo in middle of Davening?[1]

One who is in an area of Davening in which it is forbidden to make an interval, which is from Baruch Sheamar in Pesukei Dezimra until after Shemoneh Esrei, then he may not answer Baruch Hu Uvrach Shemo to a blessing.[2] [This applies even between the Perakim during Pesukei Dezimra.[3] One may not answer Baruch Hu Uvaruch Shemo even between Yishtabach and Yotzer.[4]]

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[1] Admur 124:2 in parentheses; 124:8; M”A 124:9; Beir Heiytiv 66:9; Hefsek Betefila p. 87 and 201

[2] The reason: As Baruch Hu Uvrach Shemo is a mere custom and was not instituted by the Sages. [Admur 124:8] It is therefore not considered part of the blessing [Admur 124:2] and is thus forbidden to say it in middle of Davening in any area that one may not make an interval for a mundane matter, even in those areas that it is permitted to stop and answer Amen, such as in Pesukei Dezimra. If, however, one is holding in an area of Davening that it is permitted to make an interval for even mundane matters, then it is permitted to stop and answer Baruh Hu Uvaruch Shemo. [Admur 124:8 and 2]

[3] Admur ibid “In any area that one cannot stop for a Davar Reshus”; P”M 124 A”A 9

[4] Implication of Admur ibid who compares it to Davar Shebereshus; Tehila Ledavid 124:4 that so is implied from Admur ibid, however he questions why this is the case and that seemingly one should be permitted to make an interval between Yishtabach and Yotzer to say Baruch Hu Uvaruch Shemo, just like one may stop for a Mitzvah and to say Yisbareich Veyishtabach; Hefsek Betefila p. 87 and 201

Other opinions: Some Poskim rule it is permitted to answer Baruch Hu Ubaruch Shemo between Yishtabach and Yotzer Or, being that it is permitted to make a Hefsek for the sake of a Mitzvah at this point. [Ashel Avraham Butchach 57; Darkei Chaim Veshalom 134; Lechem Salmah 36; Piskeiy Teshuvos 54:3; See Tehila Ledavid ibid and Hefsek Betefila p. 201]