LaTeX allows for three level tones and two contours to be notated using the above-vowel diacritics: \'{}
for the H tone (á), \`{}
for L (à), \={}
for M (ā), \v{}
for LH (ǎ), and \^{}
for HL (â).
The literature commonly uses above-vowel diacritics also for HM, ML, LM, MH, HLH and LHL, using sequences of the above level tones, for example a᷄ (MH) and a᷈ (LHL; note that this is not a tilde). TIPA, however, only offers tone bars for contours other than HL and LH.
Is there a way to combine diacritics in LaTeX for the combinations HM, ML, LM, MH, HLH and LHL, especially in a way available within \textipa{}
?