documentclass{article}
usepackage{accents}
usepackage{unicode-math}

newcommand{astdot}[1]{accentset{*}{#1}}
newcommand{astddot}[1]{accentset{*mkern-1mu*}{#1}}
newcommand{astdddot}[1]{accentset{*mkern-1mu*mkern-1mu*}{#1}}

newcommand{circdot}[1]{accentset{circ}{#1}}
newcommand{circddot}[1]{accentset{circmkern-1mucirc}{#1}}
newcommand{circdddot}[1]{accentset{circmkern-1mucircmkern-1mucirc}{#1}}

newcommand{genericmathaccenti}[2]{%
  genericmathaccent{#1{}}{#2}%
}
newcommand{genericmathaccentii}[2]{%
  genericmathaccent{#1{}mkern3mu#1{}}{#2}%
}
newcommand{genericmathaccentiii}[2]{%
  genericmathaccent{#1{}mkern3mu#1{}mkern3mu#1{}}{#2}%
}
newcommand{genericmathaccent}[2]{%
  vbox{offinterlineskipialign{%
    ##cr
    hidewidth$scriptstyle#1$hidewidthcr
    noalign{kern-.5ex}
    $#2$cr}%
  }%
}
newcommand{gravedot}[1]{genericmathaccenti{grave}{#1}}
newcommand{graveddot}[1]{genericmathaccentii{grave}{#1}}
newcommand{gravedddot}[1]{genericmathaccentiii{grave}{#1}}

newcommand{acutedot}[1]{genericmathaccenti{acute}{#1}}
newcommand{acuteddot}[1]{genericmathaccentii{acute}{#1}}
newcommand{acutedddot}[1]{genericmathaccentiii{acute}{#1}}

begin{document}

$astdot{x}+astddot{x}+astdddot{x}$

$circdot{x}+circddot{x}+circdddot{x}$

$gravedot{x}+graveddot{x}+gravedddot{x}$

$acutedot{x}+acuteddot{x}+acutedddot{x}$

end{document}