Is It Possible To Transfer Hosting Accounts?

Sure, it's very easy to do. Most hosts will make the transfer for you, or it's simply a matter of backing up the databases, and re-uploading those and your files to the new host's server. Then you change the IP addresses for your domain's nameservers.

That said, it's not ridiculous for a host to say that your WP plugins or WP in general is causing server problems. WP is one of the most common causes for server issues these days, in a shared environment. Non-optimized WP sites, or WP sites using a lot of plug-ins can absolutely cause server loads/issues/etc.

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