Dynamic allocation of memory uses the heap of the application/module/process (but not thread). The heap can only handle one allocation request at a time. If you try to allocate memory in "parallel" threads, they will be handled in due order by the heap. You will not get a behaviour like: one thread is waiting to get its memory while another can ask for some, while a third one is getting some. The threads will have to line-up in queue to get their chunk of memory.
What you would need is a pool of heaps. Use whichever heap is not busy at the moment to allocate the memory. But then, you have to watch out throughout the life of this variable such that it does not get de-allocated on another heap (that would cause a crash).
I know that Win32 API has functions such as GetProcessHeap(), CreateHeap(), HeapAlloc() and HeapFree(), that allow you to create a new heap and allocate/deallocate memory from a specific heap HANDLE. I don't know of an equivalence in other operating systems (I have looked for them, but to no avail).
You should, of course, try to avoid doing frequent dynamic allocations. But if you can't, you might consider (for portability) to create your own "heap" class (doesn't have to be a heap per se, just a very efficient allocator) that can manage a large chunk of memory and surely a smart pointer class that would hold a reference to the heap from which it came. This would enable you to use multiple heaps (make sure they are thread-safe).