  Coronal elemental abundances are known to deviate from the photospheric
values of their parent star, with the degree of deviation depending on the
First Ionization Potential (FIP). This study focuses on the coronal composition
of stars with super-solar photospheric abundances. We present the coronal
abundances of six such stars: 11 LMi, $\iota$ Hor, HR 7291, $\tau$ Boo, and
$\alpha$ Cen A and B. These stars all have high-statistics X-ray spectra, three
of which are presented for the first time. The abundances measured in this
paper are obtained using the line-resolved spectra of the Reflection Grating
Spectrometer (RGS) in conjunction with the higher throughput EPIC-pn camera
spectra on board the XMM-Newton observatory. A collisionally ionized plasma
model with two or three temperature components is found to represent the
spectra well. All elements are found to be consistently depleted in the coronae
compared to their respective photospheres. For 11 LMi and $\tau$ Boo no FIP
effect is present, while $\iota$ Hor, HR 7291, and $\alpha$ Cen A and B show a
clear FIP trend. These conclusions hold whether the comparison is made with
solar abundances or the individual stellar abundances. Unlike the solar corona
where low FIP elements are enriched, in these stars the FIP effect is
consistently due to a depletion of high FIP elements with respect to actual
photospheric abundances. Comparing to solar abundances (instead of stellar)
yields the same fractionation trend as on the Sun. In both cases a similar FIP
bias is inferred, but different fractionation mechanisms need to be invoked.
