It is evident that we should go on different strategies in the case of acute and chronic hypocapnia, as well as in the case of functional versus a critically ill patient.
1/ Breathing depleting drugs, such as morphine. (There are not available harmless drugs similar to this).
2/ Non-invasive pressure support ventilation (CPAP) cannot come to mind in cardiogenic pulmonary edema if hypocapnia exists, (@Valipour, see the article) only invasive mechanical ventilation.
3/ Breathing training with the biofeedback and control of PETCO2. (See @Sikter and Guevara)
https://www.researchgate.net/publication/259182574_A_Probable_Etiology_and_Pathomechanism_of_Arousal_and_Anxiety_on_Cellular_Level_-Is_It_the_Key_for_Recovering_from_Exaggerated_Anxiety
4/ A new method to normalize PETCO2 and minimize the oscillation of carbon dioxide level during Cheyne-Stokes respiration: administering low dose CO₂ in a mathematically calculated time (@Mebrate et al. 2009 see the literature of the article).
5/ An attempt to restore the original cytoplasm ion-milieu - such it was before the chronic hypocapnia started - administering physiologic salt combination in doses below of Recommended Dietary Allowance (RDA). That is the main profile of the author.
https://www.researchgate.net/publication/289460543_Modeling_of_the_Cytoplasm_English_version
6/ Certainly, the most physiological method is the right exercise training.
https://www.researchgate.net/publication/319623823_New_aspects_in_the_pathomechanism_of_diseases_of_civilization_particularly_psychosomatic_disorders_Part_1_Theoretical_background_of_a_hypothesis
Is this paper of interest to you? Int J Psychophysiol. 2010 Oct; 78(1): 68–79. doi: 10.1016/j.ijpsycho.2010.05.006PMCID: PMC2937087NIHMSID: NIHMS208631PMID: 20685222
Hyperventilation in Panic Disorder and Asthma: Empirical Evidence and Clinical Strategies
Alicia E. Meuret and Thomas Ritz
to treat the underlying pathology which has led to hypocapnia seems to me the unique solution to this issue
Do you cure all the illnesses? E.g. panic disorder? (Administration of antidepressant is not a treatment of underlying disease.)