  We construct numerically the symmetric non-Abelian wormholes which are
supported by a phantom field in the Einstein-Yang-Mills-Higgs theory beyond
Bogomol'nyi-Prasad-Sommerfield (BPS) limit where the Higgs self-interaction
constant $\lambda$ is non-vanishing. Analogous to the BPS limit, the probe
limit is the Yang-Mills-Higgs field in the background of the Ellis wormhole
when the gravity is switched off. In the presence of gravity, the wormhole
solutions possess the Yang-Mills-Higgs hair where families of hairy wormholes
solutions emerge from the Ellis wormhole when the gravitational coupling
constant increases. In contrast to the BPS limit, the properties of wormholes
change drastically when the gravitational strength approaches a critical value
for a fixed $\lambda$. The hairy wormholes possess two types of double throat
configurations. The first type is wormholes that develop the double throat when
the gravitational strength almost approaches the critical value for lower
$\lambda$, whereas the second type is wormholes that exhibit the double throat
for a certain range of gravitational strength for higher $\lambda$. These two
types of double throat configurations can coexist for a certain range of
$\lambda$ where it is a transition process for first type double throat
disappears gradually and the second type double throat becomes dominant.
