To understand this we have to go in depth , that how the ionic bond is formed?
Ionic bond is a bond basically formed due to strong electrostatic forces of attraction which is totally different from the covalent bond.
Ionic bond is formed between atoms with very different ionisation energy and electron affinity. This situation allows one atom to transfer one or more valence electrons to its partner. And that leads to generation of positive charge on donor and negative charge on accepter.
Now in case of ionic bond even if two or more electrons are transferred still the type attraction remains the same .
So they do not form double or triple bond.
But in case of Covalent bond double and triple bonds are possible.
As it involves the overlapping of orbitals and hybridization. As shown below
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