Fullerenes have potential applications in many fields. To reach their full potential, fullerenes have to be functionalized. One of the most common reactions used to functionalize fullerenes is the Diels-Alder cycloaddition. In this case, it is important to control the regioselectivity of the cycloaddition during the formation of higher adducts. In C60, successive Diels-Alder cycloadditions lead to the Th-symmetric hexakisadduct. In this work, we explore computationally using density functional theory (DFT) how the presence of a [10]cycloparaphenylene ring encapsulating C60 ([10]CPP⊃C60) affects the regioselectivity of multiple additions to C60. Our results show that the presence of the [10]CPP ring changes the preferred sites of cycloaddition compared to free C60 and leads to the formation of the tetrakisadduct. Somewhat surprisingly, our calculations predict formation of this particular tetrakisadduct to be more favored in [10]CPP⊃C60 than in free C60.