May Kaddish Derabanan of before Hodu be recited after Baruch Sheamar?
Some Poskim rule it may be recited, even if both the Minyan and the person reciting it is already after Baruch Sheamar. Other Poskim however rule it may not be recited after the Minyan has reached Baruch Sheamar, even if the person reciting on behalf of the Minyan is before Baruch Sheamar.
Minyan is before Baruch Sheamar-but the Kaddish sayer is after Baruch Sheamar: If the Minyan is before Baruch Sheamar, but the individual who desires to say the Kaddish is after Brauch Sheamar, he may not say this Kaddish. [If however he is a Yasom within 11 months of the passing of a parent, then he may recite the Kaddish even if he is past Baruch Sheamar, as explained next.]
 Kesher Gudal 7/35
 Pnei Yehoshua 1/5; Siddur Beis Oved 13; Implication of Shaar Hakavanos Derush Hakaddish; Shaareiy Teshuvah 51/3; Rav Poalim 2/14; Kaf Hachaim 53/13
 The reason: As once the Minyan has begun Pesueki Dezimra, they have lost the opportunity to say this Kaddish, as this Kaddish is meant to be said specifically before Baruch Sheamar for its spiritual effect to be utilized. [Kaf Hachaim ibid in name of Shaar Hakavanos]
 Igros Kodesh 7/139 [printed in Shulchan Menachem 1/216]
 The reason: As this is not his personal obligation, but rather the obligation of the congregation. [Rebbe ibid]
 See Shulchan Menachem ibid footnote 10