In a framework where galaxies form hierarchically, extended stellar haloes are predicted to be an ubiquitous feature around Milky Way-like galaxies and to consist mainly of the shredded stellar component of smaller galactic systems. The type of accreted stellar systems are expected to vary according to the specific accretion and merging history of a given galaxy, and so is the fraction of stars formed in situ versus accreted. Analysis of the chemical properties of Milky Way halo stars out to large Galactocentric radii can provide important insights into the properties of the environment in which the stars that contributed to the build-up of different regions of the Milky Way stellar halo formed. In this work we focus on the outer regions of the Milky Way stellar halo, by determining chemical abundances of halo stars with large present-day Galactocentric distances, >15 kpc. The data-set we acquired consists of high resolution HET/HRS, Magellan/MIKE and VLT/UVES spectra for 28 red giant branch stars covering a wide metallicity range, -3.1 ≲ [Fe/H] ≲-0.6. We show that the ratio of α-elements over Fe as a function of [Fe/H] for our sample of outer halo stars is not dissimilar from the pattern shown by MW halo stars from solar neighborhood samples. On the other hand, significant differences appear at [Fe/H] ≳-1.5 when considering chemical abundance ratios such as [Ba/Fe], [Na/Fe], [Ni/Fe], [Eu/Fe], [Ba/Y]. Qualitatively, this type of chemical abundance trends are observed in massive dwarf galaxies, such as Sagittarius and the Large Magellanic Cloud. This appears to suggest a larger contribution in the outer halo of stars formed in an environment with high initial star formation rate and already polluted by asymptotic giant branch stars with respect to inner halo samples. Based on ESO program 093.B-0615(A).Based on observations obtained with the Hobby-Eberly Telescope, which is a joint project of the University of Texas at Austin, the Pennsylvania State University, Stanford University, Ludwig-Maximilians-Universität München, and Georg-August-Universität Göttingen.This paper presents data gathered with the Magellan Telescopes at Las Campanas Observatory, Chile.Tables A.5-A.11 are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (http://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/608/A145