  Given a forcing notion $P$ that forces certain values to several classical
cardinal characteristics of the reals, we show how we can compose $P$ with a
collapse (of a cardinal $\lambda>\kappa$ to $\kappa$) such that the composition
still forces the previous values to these characteristics.
  We also show how to force distinct values to $\mathfrak m$, $\mathfrak p$ and
$\mathfrak h$ and also keeping all the values in Cicho\'n's diagram distint,
using the Boolean Ultrapower method of arXiv:1708.03691 .
  (In arXiv:2006.09826 , the same was done for the newer Cicho\'n's Maximum
construction, which avoids large cardinals.)
