seems and sentential complement

[Ash Asudeh]

Tibor,

My Canadian English confirms Shalom's Canadian English: seems does not
need a "that" complement in the examples you gave.

Interestingly, there seems to be dialectal variation with respect to this
very matter in a closely related construction: copy raising.

I've found real life corpus examples of things like this:

1) It seems like that he didn't even see us.

This is ungrammatical for me with the "that".

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Best,
Ash