Is Insprion 3671 capable of a pcie bifurcation on it's Pcie gen3 x16 slot to 8x8 or some other factors for purposes of adding a few nvme's?

There is no bifurcation available on any of Dell consumer products.

This PC only has two PCI-e x1 slots so not very fast, even if you installed an NVME SSD in an x1 adapter. 

You could add one or two 2.5" SATA3 SSDs and/or install a larger NVME SSD...

@Chino de Oro​ Are there any models that allow bifurcation such as a workstation?

There are models like XPS 8950 and XPS 8960 with two M.2 NVME slots on the motherboard for SSDs. 

And if their x4 slot is accessible (it may or not be accessible, depending on the GPU installed) you could install another NVME SSD using an x4 adapter card.

@Anbry​ , yes, selected of Precision fixed workstations starting with Haswell processors would support the lane splitting features natively.  Otherwise, only Dell enterprise class servers offer as part of scalable storage.

Alternatively, you can find a built-in switched storage controller but due to its pricey and the consumer system chassis lacks of flexbay, drive cages, making it impractical for such investment.