Hi Ajeet, one disadvantage could be the esterification of free carboxylic acids in your crude extract. I would use inert solvents like dichloromethane, dmso, dmf, acetonitrile, white spirit, cyclohexane, ethylacetate or extraction with supercritical carbondioxide. The right choice of solvent will depend on the properties of substances you will extract and the extraction conditions (e.g. temperature, duration). Do you use classical Soxleth-extraction or accelarated solvent extraction (e.g. microwave assisted). In the latter case and using e.g. solvents without a significant dipole moment (e.g. alkanes) you need indirect solvent heating by using graphite pellets.
As pointed out by Dr Christ it is possible the formation of artefacts which include also other kind of compunds in addition to the methyl esters. I.e. hydroxyl substituents in allylic configuration are reactive and may form methyl ethers; in iridoids the double bond in 3,4 position of the dihydropyran ring is also reactive and several cases of addition of methanol or other short chain alcohols in this position are reported. The reaction of strained E-double bonds upon standing in solvents has been observed also in cembranoids and under low temperature. Methyl ethers could be also formed on phenol oxydryls.
In case you are considering to freeze-dry the said methanolic extract; which may contain also water ― the following discussions may possibly be found of some help: https://www.researchgate.net/post/How_can_I_dry_a_methanolic_extract/1 https://www.researchgate.net/post/Can_using_methanol_damage_a_freeze-drier_machine