I wonder how is it possible to construct a language based on the existing languages. There are Indo-European, Altaic, Semitic, and a small portion of Dravidian and Caucasic languages in my country, and I am thinking of a constructed language based on all of these languages.
Possible? Definitely yes!
But I want to give you some more hints on how to do it:
Base on common features: When choosing the sounds for your conlang, prefer those sounds that have a broad coverage in your language base, and avoid those the are specific to only one of them. Do the same for syllable structure, look what consonants can cluster with each other in a lot of your base languages.
Select common words: Look what words already have crossed the language boundaries and appear as loan words in other languages. These words are hot candidates for inclusion in your conlang. Note also that the process of loaning words tends to result in phonological and morphological simplifications, consider adopting these simplifications as well.
Morphology: Look for common categories expressed by morphology in the base languages, and use a simplified system of them. While Arabic morphology (inflectional and derivational) is elegant and impressive, it does not carry over to languages with a different structure (no triconsonantal roots) well. But you still can borrow some elements from it (e.g., prefixes and suffixes). Make sure to create at least some derivational morphology, it will simplify the language and the process of creating the vocab.
Syntax: Check out the basic word order and the way how to form relative clauses and subordinate clauses in your base language, and create a syntax from this information. Also look for word order phenomena (adjectives before or after the noun, prepositions or postpositions, genitives before or after the noun) and decide how to do them.
There should be no problem in doing so -- just mix and match features from the various source languages. A precedent for this for example is English:
- the syntax/grammar is mainly Germanic, including many function words
- the vocabulary is mixed (Latin, Norse, Anglo-Saxon, Norman French, Indian, ...)
I would choose on language as the "base" (in the English case it's Old English/Anglo-Saxon), and then modify it by replacing/adding some of the vocabulary from the different languages. Also, some grammatical features (morphological endings etc) could be mixed up.
If you do it iteratively (ie revising the language multiple times, simulating contact between the current version and another influencing language), you can also take into account other types of changes, such as dropping endings which are harder to pronounce, or making higher frequent words shorter and less regular.
What you do exactly is up to you, but there shouldn't be any problem from a linguistic point of view.