Overcalling

♣ ♦ ♥ ♠

Our RH opponent opened a natural 1♣ 1♦ 1♥ 1♠

Over an opponents 1♣ 1♦ opening BETA o'calls with Double to indicates that if it were our opening bid we would have opened 1♣ or 1N ourselves! See specifications given in 1C continuations.
However take note the use 1-level transfer responses over an opponents 1C opening and * shows our 1C BETA opening. Also: As a 1NT o'call signals a BETA multi 1NT a BETA 1N opening should now be introduced by doubling 1C and rebid of 1N.
If LHO passes our '*' or redoubles partner uses our transfer reponses as per our 1C opening specification:
[D=H, H=S, S=D].
and our subsequent bidding follows our 1C sequences.
Also if LHO bids 1D|1H|1S then * shows 4+ Hearts, 4+ Spades & 4+ Hearts respectively - as defined for a 1C opening continuations follow as defined for a 1C opening.
rebids now as defined for 1C openings.
One reminder: if our opponents 1♣! is alerted as strong - 16+ HCP then we employ TRAP.