I quote from B. Elizabeth Pryce's excellent book "How Good Is Your English?" (1985) :-

Countable nouns can carry indications of large or small numbers by the use of words few, a few, many.. Few means a very small amount where more might have been expected. A few means only a small number where hardly any might be expected. Many means a good number, more than several.

There have been few oranges in the trees this year, in fact a very disappointing crop.

There were still a few oranges left on the trees after they had all been picked for marketing.

There are many oranges on the trees this year, promising a good crop.

So. The answer to your question appears to be that it is grammatically correct to "invite many people" to a party.