Sure its possible, lots of us do.
People explain these beliefs in different ways. Some consider themselves "eclectic," some "interfaith," some "Universalist," and so on. I consider myself AllFaith, hence, John of AllFaith and AllFaith.com.
Among the differences is how we view the various religions. Many people do as you suggest, they combine the various religions into something new. I would not call this foolish, it works quite likely for some people, even though it is the Path I follow.
My view is that there is but One God and the Holy One has historically revealed truth in terms of human cultures and readiness, in ways the diverse groups could appreciate and accept. Despite this, God is One. As the Rg. Veda puts it, "Truth is One, the sages call it by different names."
In my opinion the various religions are all holders of the One Truth. Without appreciating the cultural and historic aspects of the various religions it is difficult if not impossible to fully appreciate the Truth they contain.
For this reason I have converted into most of the major religions and learned their essential teachings from their perspectives, as well of course as reading a lot, receiving degrees etc.
I don't try to combine the religions, I try to understand them separately, honoring their unique traditions.
What I believe personally is what I have realized through these diverse teachings and through my own meditations and experiences. My beliefs are therefore uniquely my own.
It's certainly easier and just as effective to devote oneself to a single path. God looks at the heart. For some of us however it is clearly the leading of the Holy One that we follow a more eclectic spirituality. I see nothing foolish about it, however as the Apostle Paul says:
"God hath chosen the foolish things of the world to confound the wise; and God hath chosen the weak things of the world to confound the things which are mighty" (I Cor. 1:25).
I am confident in the Path I follow.
God's Garden
by John of AllFaith © 1979
Some folks say they know the truth
They claim they've got it all down,
But I say that such people
Are little more than clowns
For God is far greater
Than anything, we conceive
And so we're only partly right
No matter what we believe
Like Paul we gaze in the mirror
And behold our own reflection
I guess we won't really know the Truth
'Till we attain perfection
The only thing I know for sure
Is that God is Love
My only hope of salvation
Is to trust that Love above
Yah vishva deva
Ki vatika
Hai sair karne
Ke liye
[translation: This universe is God's garden
And it's meant for roaming in]