as i speak chinese near to a Native level .
i can say that Thai don't have the question that you ask: 3 tones + 3 tones first 3 tones Must change to 2 tones,
also the word 不 is change too when combined with 3tone and 4 tone.
however, as you know Thai tones don't change according to the word following.
but Thai, word do change tones in some conditions.
all the Thai alphabets devided into 3 group,
1) high tone alphabets
2) medow tone alphabets
3) low tone alphabets
so, keep in mind, the 2)group always the same, they can make 5tones in THai,
but the 1) and 3) groups alphabets some can't match 5 tones,
so the tricky is here, they will not read as the tone appeared.
this is conpricated topic, even Many for many thai.
but, it is not too hard.
take your times :)
good luck ， ｓａｂａｓｉｂｏ