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Graphene doped by alkali atoms (AC<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mi>x</mi></msub></semantics></math></inline-formula>) supports two heavily populated bands (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>π</mi></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>σ</mi></semantics></math></inline-formula>) crossing the Fermi level, which enables the formation of two intense two-dimensional plasmons: the Dirac plasmon (DP) and the acoustic plasmon (AP). Although the mechanism of the formation of these plasmons in electrostatically biased graphene or at noble metal surfaces is well known, the mechanism of their formation in alkali-doped graphenes is still not completely understood. We shall demonstrate that two isoelectronic systems, KC<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>8</mn></msub></semantics></math></inline-formula> and CsC<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>8</mn></msub></semantics></math></inline-formula>, support substantially different plasmonic spectra: the KC<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>8</mn></msub></semantics></math></inline-formula> supports a sharp DP and a well-defined AP, while the CsC<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>8</mn></msub></semantics></math></inline-formula> supports a broad DP and does not support an AP at all. We shall demonstrate that the AP in an AC<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mi>x</mi></msub></semantics></math></inline-formula> is not, as previously believed, just a consequence of the interplay of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>π</mi></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>σ</mi></semantics></math></inline-formula> intraband transitions, but a very subtle interplay between these transitions and the background screening, caused by the out-of-plane interband <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>C</mi><mo>(</mo><mi>π</mi><mo>)</mo><mo>→</mo><mi>A</mi><mo>(</mo><mi>σ</mi><mo>)</mo></mrow></semantics></math></inline-formula> transitions.