Rocket staging by use of strap on Boosters

Question

Will it be advantageous to have multiple (say-3) stages of a rocket, arranged in a "strap-on" type SRBs' assembly, geometrically well distributed around the circumference w.r.t. their numbers in each "stage" (though their ignition/firing will be sequential i.e. in series) - instead of arranging them one over the other? Will such an arrangement pose any problems in "steering" of the rocket (presuming SRBs do not have a gimbled nozzle)

Answer 1

Will it be advantageous to have multiple (say-3) stages of a rocket, arranged in a "strap-on" type SRBs' assembly, geometrically well distributed around the circumference

There's a small disadvantage; the aerodynamic cross-section of such a rocket is larger than a longitudinally staged rocket, so it loses more energy to air resistance.

Side-mounted liquid-fueled boosters do offer the possibility of propellant cross-feed, using the fuel stored in the outer boosters to fill the inner ones during concurrent burns, but there's no advantage in sequential burns.

Will such an arrangement pose any problems in "steering" of the rocket (presuming SRBs do not have a gimbled nozzle)

You need some sort of steering method; modern SRBs on large launchers, as Organic Marble points out, usually do have gimbaled nozzles. Moving fins or secondary steerable thrusters are the other common options, but gimbaled nozzles are generally the most efficient solution.

The more compact arrangement you describe requires somewhat more sideways thrust force (from gimbals, fins, or thrusters) to turn the booster in flight -- another slight disadvantage.