Depending on weight (mass for you European folks), altitude, and ambient temperature, it is possible to contine the climb, with two engines failed, on the same side.
Possible with the B707, and B747.
An example.
Circa 1985, location JED, type B747SP.
Max AUW, departing 34L, ambient temperature 28C.
At 200 agl, severe vibs from number two.
Number two throttle retarded, vibs decreased (as would be expected).
Throttle advanced again (bad idea) at 400 agl.
Severe vibs again from number two, then bang.
Number two now finished, and bits from number two migrated to number one.
Number one still producing rated thrust, however the F/E notices that number one fire pull handle red light is eluminated, but no fire bell.
Without saying anything, F/E now acts on his own, and pulls number one fire pull handle.
Resultant configuration: 800 agl, on two engines only (3&4).
Captain (PF) starts slow descent, requests flap retraction on speed schedule, requests immediate fuel dumping.
Clean speed reached at 200 agl, and a very shallow climb established, for a return for landing.
Aircraft landed 34L, without futher incident using reduced flap setting.
As can be seen, a failure of two engines in the immediate climb after takeoff can be accomplished successfully, if flown correctly.
Very doubtful with two engines failed while on the runway...at all but the lowest of weights.