We analyse configurations of compact stars in the so-called R-squared gravity in the Palatini formalism. Using a realistic equation of state we show that the mass-radius configurations are lighter than their counterparts in General Relativity. We also obtain the internal profiles, which run in strong correlation with the derivatives of the equation of state, leading to regions where the mass parameter decreases with the radial coordinate in a counter-intuitive way. In order to analyse such correlation, we introduce a parametrisation of the equation of state given by multiple polytropes, which allows us to explicitly control its derivatives. We show that, even in a limiting case where hard phase transitions in matter are allowed, the internal profile of the mass parameter still presents strange features and the calculated M-R configurations also yield NSs lighter than those obtained in General Relativity.
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