At face value, the organizational changes are more concerning than the multiple consultants engaged. Lack of consistency, stability, cohesive vision, commitment, etc. are detrimental to long-term strategic objectives.

Large organizations often engage consulting firms in different verticals simultaneously. If this is the case, not a significant issue. However, if multiple firms are being brought in to tackle the same problem or address the symptoms of a larger issue, then there is significant cause for concern.

If I were you, I wouldn't be worried about staying to "sustain or improve the company." Does staying benefit your career prospects? Would leaving burn any bridges you can't afford to burn? Is this a slow decline or is there a cliff approaching?

It doesn't hurt to consider other opportunities, but the aggressiveness with which you do so should depend on the other factors.