Anyway, the more compositions there are, the bigger the challenge to come up with something new. The invention of a new theme might still be possible, yet it's quite rare. You can rather see that existing themes are varied and/or combined.
In his booklet Caissa's Wild Roses in Clusters (published 1937), Thomas Rayner Dawson discusses the field of theme transformations often making use of fairy chess elements. I've selected some "big" problems for you. Enjoy! Please bear in mind that only the thematic variations are mentioned.
The first three examples deal with the Grimshaw theme, named after the 19th century problem composer Walter Grimshaw. A Grimshaw denotes the mutual interference of two different types of pieces of the same colour arriving on a particular square. By the way, the referenced Wikipedia article wrongly states that a Grimshaw only deals with Black interferences, but there are also white Grimshaws! Anyway, it features some nice orthodox problems.

1. Nm2! (threats 2. Nc7#). Black defends by blocking the nightrider's route to c7 on k3 thus inducing a triple Grimshaw:
1.  Rk3 2. Rm3#
1.  Bk3 2. Ri5#
1.  Nk3 2. Rj5#
Each of the thematic black pieces observes a certain square in order to defend against a checkmate by the Nq3. The defenses are Nl1i7, Bm1c9 and Rh3xq3. The Grimshaw interference on k3 deactivates two of these moves, so that the white rook can take care of the third and deliver a discovered mate.

1. Ne7! This nightrider covers the check by the Na15 thus pinning itself. The thematic variations are
1.  Nb13,c12,d11 2. Qxe10# Qa14 blocked.
1.  Nc11,d10,e9 2. Nxf8# Bb12 blocked.
1.  Nd9,e8,f7 2. Qg6# Bc10 blocked.
1.  Qb13,Bc11,Bd9 2. Ni5# Na15 blocked.
1.  Qc12,Bd10,Be8 2. Nxf6# Nb14 blocked.
1.  Qd11,Be9,Bf7 2. S4g5# Nc13 blocked.
The three parallel lines of the nightriders (a15h1, b14f6, c13g5) are cut by the three parallel lines of the queen and the two bishops (a14e10, b12f8, c10g6) and vice versa. Dawson calls this a polylinear Grimshaw.

Here, we see a triple mutual Grimshaw.
1. Rk16! covers the check from Na11.
1.  Nc10 2. Nxb9#
1.  Bc10 2. Na1#
1.  Nc12 2. Nb13#
1.  Bc12 2. Ne13#
1.  Ng14 2. Nh15#
1.  Bg14 2. Rxk11#
The aim of the Black defenses is to get a flight for his king. Moving to c10, Black unguards e10, the interference on c12 unguards f12 and playing a piece to g14 unguards g11. White answers by firing the three batteries Re2/Ne3, Rf8/Nf15 and Bo19/Nn18, respectively, corresponding to the flights. There's just the last variation whithout a battery firing, too bad.
The last two problems demonstrate the maximum mates by a grasshopper and a nightrider, respectively.

After 1. Kf10! Black is in zugzwang:
1.  Gg6 2. Gg7#
1.  Gg8 2. Gg9#
1.  Gg10 2. Gg11#
1.  h4 2. Gi5#
1.  j6 2. Gk7#
1.  l8 2. Gm9#
1.  j3 2. Gi3#
1.  h(xg)2, Gh2 2. Go3#
1.  Gh2 2. Gi1#
1.  d3 2. Gc3#
1.  f4 2. Ge5#
1.  f8 2. Ga9#
We see the maximum of 12 mates by a grashopper.

1. Bj7! (threats 2. Rk10#)
1.  Nc9 2. Nc12#
1.  Nc7 2. Na7#
1.  Nd2 2. Nc2#
1.  Nm2 2. Nk2#
1,  Sm11 2. Nxm7#
1.  Sl12 2. Nxk12#
All mates exploit Black selfinterferences. Dawson points out that the absolute maximum of 12 mates by a nightrider can be achieved on a board not less than 101 by 121. Any takers?
2 comments:
Enjoyed your comments and explanation of the grimshaw theme of the great T.R.Dawson. Thanks.
Thanks for your detailed explanation of the TRD problems. I enjoyed it.
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