This might be considered as a duplicate of a thorough explanation of various approaches, however I can\'t seem to find a solution to my problem there due to a higher number
I would use append.
>>> df1.append(df2).append(df3).sort_values('depth')
VAR1 VAR2 VAR3 depth profile
0 38.196202 NaN NaN 0.5 profile_1
1 38.198002 NaN NaN 0.6 profile_1
0 NaN 0.20440 NaN 0.6 profile_1
1 NaN 0.20442 NaN 1.1 profile_1
2 NaN 0.20446 NaN 1.2 profile_1
0 NaN NaN 15.188 1.2 profile_1
2 38.200001 NaN NaN 1.3 profile_1
1 NaN NaN 15.182 1.3 profile_1
2 NaN NaN 15.182 1.4 profile_1
Obviously if you have a lot of dataframes, just make a list and loop through them.