Yes. Under Sec.65.1 of the IRR, there are at least 2 grounds when a criminal action may be filed (by BAC) against the HoPE.
65.1 Without prejudice to the provisions of R.A. 3019 and other penal laws, public officers who commit any of the following acts shall suffer the penalty of imprisonment of not less than six (6) years and one (1) day, but not more than fifteen (15) years:
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c) Unduly influencing or exerting undue pressure on any member of the BAC or any officer or employee of the Procuring Entity to take a particular action which favors, or tends to favor a particular bidder.
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e) Abuse by the HoPE of his power to reject any and all bids as mentioned under Section 41 of the Act and this IRR, with manifest preference to any bidder who is closely related to him in accordance with Section 47 of the Act and this IRR.
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But the real question is the practicality of the action. Remember that the HopE is the one who designated the BAC members. The HoPE, being the head of agency, has also inherent disciplinary action against its employees. An action against the HoPE filed by the BAC can be taken as "an act of war" that usually does not end well, especially if the foundation and evidence is not that strong.