Have you deleted problematic indicators in first order and second order models? If not then apply these and then check MSV.
1. First-order measurement items to be deleted:
i) delete non-significant loadings on the hypothesized sub-dimensions as such loadings indicate poor or lack of validity,
ii) delete standardized loadings that are less than .50;
iii) also delete large and significant measurement error co-variances with other measures (especially measures of other sub-dimensions) as such measurement error co-variances reflect multidimensionality. The covariance values can be checked using modification indices.
iv) also delete large and significant cross-loadings on non-hypothesized sub-dimensions as these indicate conceptual confounding. These values can also be checked using modification indices.
2. First-order sub-dimensions that have weak or non-significant loadings on the second-order construct can also be deleted with justification as sometimes this may result in lack of validity.
For establishing discriminant validity, see if AVE of a construct is greater than the squared correlation between the construct and conceptually similar construct. See the paper by Fornell and Larcker (1981).