Are there any celestial bodies beyond the Local Group can cause of blue shift? Is it possible?

Yes. While celestial objects at that distance moving towards us might be rare, rotation objects might be fast enough to have one side blushifted, especially accretion disks and pulsars. Also, pulsars with the gas jets pointed towards us, and black holes/quasars (Blazars) with gas jets pointed towards us, might appear partially blueshifted, as the jets would be travelling extremely fast, possibly at relativistic speeds, and appear blueshifted. There are, of course, candidates of galaxies outside the local group actually blueshifted, such as IC 3258. There is, however, sure no way of identifying whether they are dwarves in the Local Group or giants outside, and fitting the galaxy into existing knowledge only tells us it's "probably" a giant.