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Pressure shifts inside an atomic beam are among the more theoretically challenging effects in high-precision measurements of atomic transitions. A crucial element in their theoretical analysis is the understanding of long-range interatomic interactions inside the beam. For excited reference states, the presence of quasi-degenerate states leads to additional challenges, due to the necessity to diagonalize large matrices in the quasi-degenerate hyperfine manifolds. Here, we focus on the interactions of hydrogen atoms in reference states composed of an excited <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mi>D</mi></mrow></semantics></math></inline-formula> state (atom <i>A</i>), and in the metastable <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2</mn><mi>S</mi></mrow></semantics></math></inline-formula> state (atom <i>B</i>). We devote special attention to the cases <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>=</mo><mn>3</mn></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>=</mo><mn>8</mn></mrow></semantics></math></inline-formula>. For <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>=</mo><mn>3</mn></mrow></semantics></math></inline-formula>, the main effect is generated by quasi-degenerate virtual <i>P</i> states from both atoms <i>A</i> and <i>B</i> and leads to experimentally relevant second-order long-range (van-der-Waals) interactions proportional to the sixth inverse power of the interatomic distance. For <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>=</mo><mn>8</mn></mrow></semantics></math></inline-formula>, in addition to virtual states with two states of <i>P</i> symmetry, one needs to take into account combined virtual <i>P</i> and <i>F</i> states from atoms <i>A</i> and <i>B</i>. The numerical value of the so-called <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>C</mi><mn>6</mn></msub></semantics></math></inline-formula> coefficients multiplying the interaction energy was found to grow with the principal quantum number of the reference <i>D</i> state; it was found to be of the order of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mn>10</mn><mn>11</mn></msup></semantics></math></inline-formula> in atomic units. The result allows for the calculation of the pressure shift inside atomic beams while driving transitions to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mi>D</mi></mrow></semantics></math></inline-formula> states.